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Analytic shock‐fronted solutions to a reaction–diffusion equation with negative diffusivity Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-21 Thomas Miller, Alexander K. Y. Tam, Robert Marangell, Martin Wechselberger, Bronwyn H. Bradshaw‐Hajek
Reaction–diffusion equations (RDEs) model the spatiotemporal evolution of a density field according to diffusion and net local changes. Usually, the diffusivity is positive for all values of , which causes the density to disperse. However, RDEs with partially negative diffusivity can model aggregation, which is the preferred behavior in some circumstances. In this paper, we consider a nonlinear RDE
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Sharp thresholds of blowup and uniform bound for a Schrödinger system with second‐order derivative‐type and combined power‐type nonlinearities Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-20 Kelin Li, Huafei Di
Considered herein is a Cauchy problem for a system of Schrödinger equations with second‐order derivative‐type and combined power‐type nonlinearities. Through the effective combination of potential well theory, conservation laws, and vector‐valued Gargliardo–Nirenberg inequality, we establish the uniform boundedness in ‐norm on and corresponding decay rate estimate. Moreover, we also prove the existence
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Quantitative analysis of passive intermodulation and surface roughness Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-19 Eric Stachura, Niklas Wellander, Elena Cherkaev
We explore the relationship between rough surface conductors and the phenomenon of passive intermodulation. The underlying surface is taken to be the boundary of a Lipschitz domain, and a characteristic angle of the domain is used to track boundary dependence on the various fields. To model electro‐thermal passive intermodulation in particular, we consider a specific type of temperature‐dependent conductivity
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Rigorous derivation of weakly dispersive shallow‐water models with large amplitude topography variations Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-18 Louis Emerald, Martin Oen Paulsen
We derive rigorously from the water waves equations new irrotational shallow‐water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the possible change in the waves' propagation, which can occur in the case of large amplitude topography. The main contribution of this work is the construction of new multiscale
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Kirillov structures and reduction of Hamiltonian systems by scaling and standard symmetries Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-11 A. Bravetti, S. Grillo, J. C. Marrero, E. Padrón
In this paper, we discuss the reduction of symplectic Hamiltonian systems by scaling and standard symmetries which commute. We prove that such a reduction process produces a so‐called Kirillov Hamiltonian system. Moreover, we show that if we reduce first by the scaling symmetries and then by the standard ones or in the opposite order, we obtain equivalent Kirillov Hamiltonian systems. In the particular
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On an SIS epidemic model with power‐like nonlinear incidence and with/without cross‐diffusion Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-11 Huicong Li, Tian Xiang
We study global existence, boundedness, and convergence of nonnegative classical solutions to a Neumann initial‐boundary value problem for the following possibly cross‐diffusive SIS (susceptible–infected–susceptible) epidemic model with power‐like infection mechanism generalizing the standard mass action incidence: in a bounded smooth domain . The infection force of the form with is a natural extension
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A free boundary problem with resource‐dependent motility in a weak heterogeneous environment Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-09 Dawei Zhang, Yun Huang, Chufen Wu, Jianshe Yu
This paper is concerned with a free boundary problem with resource‐dependent motility in a weak heterogeneous environment. The existence and uniqueness of global solutions are discussed first. Next, we establish long‐time behaviors of solutions which is a spreading–vanishing dichotomy. Moreover, we obtain sharp criteria on spreading and vanishing by investigating the associated linearized eigenvalue
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Multiloop soliton solutions and compound WKI–SP hierarchy Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-08 Xiaorui Hu, Tianle Xu, Junyang Zhang, Shoufeng Shen
In this paper, a compound equation which is a mix of the Wadati–Konno–Ichikawa (WKI) equation and the short‐pulse (SP) equation is first studied. By transforming both the independent and dependent variables in the equation, we introduce a novel hodograph transformation to convert the compound WKI–SP equation into the mKdV–SG (modified Korteweg–de Vries and sine‐Gordon) equation. The multiloop soliton
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Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-05 Huiping Zang, Yi Lin, Shengqiang Liu
Many epidemic models assume an exponential distribution for the latent stage, but this may not accurately represent reality and could impact disease transmission predictions. Previous studies for short time scale models have shown that the choice of latency distribution affects estimates of the epidemic peak, time to peak, and infection eradication time, but has little effect on the final infection
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Spectral and linear stability of peakons in the Novikov equation Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-05 Stéphane Lafortune
The Novikov equation is a peakon equation with cubic nonlinearity, which, like the Camassa–Holm and the Degasperis–Procesi, is completely integrable. In this paper, we study the spectral and linear stability of peakon solutions of the Novikov equation. We prove spectral instability of the peakons in . To do so, we start with a linearized operator defined on and extend it to a linearized operator defined
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N‐fold Darboux transformation of the discrete PT‐symmetric nonlinear Schrödinger equation and new soliton solutions over the nonzero background Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-05 Tao Xu, Li‐Cong An, Min Li, Chuan‐Xin Xu
For the discrete PT‐symmetric nonlinear Schrödinger (dPTNLS) equation, this paper gives a rigorous proof of the N‐fold Darboux transformation (DT) and especially verifies the PT‐symmetric relation between transformed potentials in the Lax pair. Meanwhile, some determinant identities are developed in completing the proof. When the tanh‐function solution is directly selected as a seed for the focusing
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Spectral Jacobi approximations for Boussinesq systems Stud. Appl. Math. (IF 2.7) Pub Date : 2024-03-02 Angel Duran
This paper is concerned with the numerical approximation of initial‐boundary‐value problems of a three‐parameter family of Bona–Smith systems, derived as a model for the propagation of surface waves under a physical Boussinesq regime. The work proposed here is focused on the corresponding problem with Dirichlet boundary conditions and its approximation in space with spectral methods based on Jacobi
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Asymptotic profiles of a spatial vector‐borne disease model with Fokker–Planck‐type diffusion Stud. Appl. Math. (IF 2.7) Pub Date : 2024-02-20 Kai Wang, Hongyong Zhao, Hao Wang
This paper is concerned with a spatially heterogeneous vector‐borne disease model that follows the Fokker–Planck‐type diffusion law. One of the significant features in our model is that Fokker–Planck‐type diffusion is used to characterize individual movement, which poses new challenges to theoretical analysis. We derive for the first time the variational characterization of basic reproduction ratio
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Bifurcations and global dynamics of a predator–prey mite model of Leslie type Stud. Appl. Math. (IF 2.7) Pub Date : 2024-02-15 Yue Yang, Yancong Xu, Libin Rong, Shigui Ruan
In this paper, we study a predator–prey mite model of Leslie type with generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focus-type and cusp-type degenerate Bogdanov–Takens bifurcations of codimension 3, originating from a nilpotent focus or cusp of codimension
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The Riemann–Hilbert approach for the integrable fractional Fokas–Lenells equation Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-28 Ling An, Liming Ling
In this paper, we propose a new integrable fractional Fokas–Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the Riemann–Hilbert approach. Specifically, we focus on the case of the reflectionless potential with a simple pole for the zero boundary condition. And we provide the fractional
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On the dynamics of an epidemic patch model with mass-action transmission mechanism and asymmetric dispersal patterns Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-28 Rachidi B. Salako, Yixiang Wu
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number R 0 $\mathcal {R}_0$ is less than one and the dispersal rate of the susceptible population d S
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Global well-posedness and long-time behavior in a tumor invasion model with cross-diffusion Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-18 Chunhua Jin
This paper is concerned with a cross-diffusion tumor invasion model with double-taxis effect. We first investigate the global existence of classical solutions of this model in two-dimensional space. The essential difficulty lies in the second-level taxis effect of immune cells on tumor cells, where chemotactic factor (tumor cells) exhibit their own taxis behavior, the double-taxis effect makes us have
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Multidomain spectral approach to rational-order fractional derivatives Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-18 Christian Klein, Nikola Stoilov
We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Z q $Z_{q}$ curve ensuring analyticity of the respective integrands, the integrals over
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Unveiling measles transmission dynamics: Insights from a stochastic model with nonlinear incidence Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-18 Zhenfeng Shi, Daqing Jiang
In this paper, taking into account the inevitable impact of environmental perturbations on disease transmission, we primarily investigate a stochastic model for measles infection with nonlinear incidence. The transmission rate in this model follows a logarithmic normal distribution influenced by an Ornstein–Uhlenbeck (OU) process. To analyze the dynamic properties of the stochastic model, our first
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Asymptotic spatial behavior for the heat equation on noncompact regions Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-16 Robin J. Knops, Ramon Quintanilla
We consider the isotropic initial boundary value problem for the heat equation on open regions with noncompact boundary and construct differential inequalities for a generalized heat flow measure defined over a spherical cross section. Under suitable assumptions, integration of the differential inequality leads to spatial growth and decay rate estimates for mean-square cross-sectional measures of the
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Inversion formula for an integral geometry problem over surfaces of revolution Stud. Appl. Math. (IF 2.7) Pub Date : 2024-01-02 Zekeriya Ustaoglu
An integral geometry problem is considered on a family of n$n$-dimensional surfaces of revolution whose vertices lie on a hyperplane and directions of symmetry axes are fixed and orthogonal to this plane, in Rn+1$\mathbb {R} ^{n+1}$. More precisely, the reconstruction of a function f(x,y)$f(\mathbf {x,}y)$, x∈Rn$\mathbf {x}\in \mathbb {R} ^{n}$, y∈R$y\in \mathbb {R}$, from the integrals of the form
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Resurgent aspects of applied exponential asymptotics Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-26 Samuel Crew, Philippe H. Trinh
In many physical problems, it is important to capture exponentially small effects that lie beyond-all-orders of an algebraic asymptotic expansion; when collected, the full asymptotic expansion is known as a trans-series. Applied exponential asymptotics has been enormously successful in developing practical tools for studying the leading exponentials of a trans-series expansion, typically for singularly
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Long-time asymptotics and the radiation condition with time-periodic boundary conditions for linear evolution equations on the half-line and experiment Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-22 Yifeng Mao, Dionyssios Mantzavinos, Mark A. Hoefer
The asymptotic Dirichlet-to-Neumann (D-N) map is constructed for a class of scalar, constant coefficient, linear, third-order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half-line, modeling a wavemaker acting upon an initially quiescent medium. The large time t$t$ asymptotics for the special cases of the linear Korteweg-de Vries and linear
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Instability of near-extreme solutions to the Whitham equation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-19 John D. Carter
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths in shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute 2π-periodic traveling wave solutions of the Whitham equation and numerically study their stability with a focus on solutions with large steepness.
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Predator–prey model with sigmoid functional response Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-19 Wei Su, Xiang Zhang
The sigmoid functional response in the predator–prey model was posed in 1977. But its dynamics has not been completely characterized. This paper completes the classification of the global dynamics for the classical predator–prey model with the sigmoid functional response, whose denominator has two different zeros. The dynamical phenomena we obtain here include global stability, the existence of the
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Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-19 Bashar Khorbatly, Henrik Kalisch
It is shown that the Boussinesq–Peregrine system, which describes long waves of small amplitude at the surface of an inviscid fluid with variable depth, admits a number of approximate conservation equations. Notably, this paper provides accurate estimations for the approximate conservation of the mechanical balance laws associated with mass, momentum, and energy. These precise estimates offer valuable
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Dynamics of 2D fluid in bounded domain via conformal variables Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-12 Alexander Chernyavsky, Sergey Dyachenko
In the present work, we compute numerical solutions of an integro-differential equation for traveling waves on the boundary of a 2D blob of an ideal fluid in the presence of surface tension. We find that solutions with multiple lobes tend to approach Crapper capillary waves in the limit of many lobes. Solutions with a few lobes become elongated as they become more nonlinear. It is unclear whether there
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Multisoliton interactions approximating the dynamics of breather solutions Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-11 Dmitry Agafontsev, Andrey Gelash, Stephane Randoux, Pierre Suret
Nowadays, breather solutions are generally accepted models of rogue waves. However, breathers exist on a finite background and therefore are not localized, while wavefields in nature can generally be considered as localized due to the limited sizes of physical domain. Hence, the theory of rogue waves needs to be supplemented with localized solutions, which evolve locally as breathers. In this paper
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Matrix exceptional Laguerre polynomials Stud. Appl. Math. (IF 2.7) Pub Date : 2023-12-08 E. Koelink, L. Morey, P. Román
We give an analog of exceptional polynomials in the matrix-valued setting by considering suitable factorizations of a given second-order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence are discussed in detail. We give an example of matrix-valued exceptional Laguerre polynomials of arbitrary size.
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Landscape of wave focusing and localization at low frequencies Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-28 Bryn Davies, Yiqi Lou
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems that resonate in a subwavelength regime. Our from-first-principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving
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KP reductions and various soliton solutions to the Fokas–Lenells equation under nonzero boundary condition Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-23 Yujuan Zhang, Ruyun Ma, Bao-Feng Feng
In this paper, we clarify the connection of the Fokas–Lenells (FL) equation to the Kadomtsev–Petviashvili (KP)–Toda hierarchy by using a set of bilinear equations as a bridge and confirm multidark soliton solution to the FL equation previously given by Matsuno (J. Phys. A 2012 45 (475202). We also show that the set of bilinear equations in the KP–Toda hierarchy can be generated from a single discrete
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Two-dimensional Riemann problem of the Euler equations to the Van der Waals gas around a sharp corner Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-22 Shuangrong Li, Wancheng Sheng
In this paper, we study the Riemann problem of the two-dimensional (2D) pseudo-steady supersonic flow with Van der Waals gas around a sharp corner expanding into vacuum. The essence of this problem is the interaction of the centered simple wave with the planar rarefaction wave, which can be solved by a Goursat problem or a mixed characteristic boundary value and slip boundary value problem for the
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Construction of inclusions with vanishing generalized polarization tensors by imperfect interfaces Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-22 Doosung Choi, Mikyoung Lim
We investigate the problem of planar conductivity inclusion with imperfect interface conditions. We assume that the inclusion is simply connected. The presence of the inclusion causes a perturbation in the incident background field. This perturbation admits a multipole expansion of which coefficients we call as the generalized polarization tensors (GPTs), extending the previous terminology for inclusions
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Doubly localized two-dimensional rogue waves generated by resonant collision in Maccari system Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-21 Yulei Cao, Jingsong He, Yi Cheng
In this paper, the Maccari system is investigated, which is viewed as a two-dimensional extension of nonlinear Schrödinger equation. We derive doubly localized two-dimensional rogue waves on the dark solitons of the Maccari system with Kadomtsev–Petviashvili hierarchy reduction method. The two-dimensional rogue waves include line segment rogue waves and rogue-lump waves, which are localized in two-dimensional
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Global existence and the time decay estimates of solutions to the compressible quantum Navier–Stokes–Maxwell system in R3 Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-17 Leilei Tong, Miao Luo
We consider the Cauchy problem of the compressible quantum Navier–Stokes–Maxwell equations with the linear damping in the isentropic case under the small perturbation of the constant equilibrium state in three dimensions. Based on the refined energy method, we establish the classical solution globally in time in Sobolev space. By the combination of the energy estimates with the interpolation between
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Whitham modulation theory for the Zakharov–Kuznetsov equation and stability analysis of its periodic traveling wave solutions Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-16 Gino Biondini, Alexander Chernyavsky
We derive the Whitham modulation equations for the Zakharov–Kuznetsov equation via a multiple scales expansion and averaging two conservation laws over one oscillation period of its periodic traveling wave solutions. We then use the Whitham modulation equations to study the transverse stability of the periodic traveling wave solutions. We find that all periodic solutions traveling along the first spatial
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The Airy equation with nonlocal conditions Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-14 B. Normatov, D. A. Smith
We study a third-order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed, we use a nonlocal condition, which specifies a weighted integral of the solution over the spatial interval. Via adaptations of the Fokas transform method (or unified
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A mean-field approach for the asymptotic tracking problem of moving continuum target clouds Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-14 Hyunjin Ahn, Seung-Yeal Ha
We propose a new coupled kinetic system arising from the asymptotic tracking of a continuum target cloud, and study its asymptotic tracking property. For the proposed kinetic system, we present an energy functional which is monotonic and distance between particle trajectories corresponding to kinetic equations for target, and tracking ensembles tend to zero asymptotically under a suitable sufficient
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The effects of viscosity on the linear stability of damped Stokes waves, downshifting, and rogue wave generation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-11-13 A. Calini, C. L. Ellisor, C. M. Schober, E. Smith
We investigate a higher order nonlinear Schrödinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we discuss how the viscosity affects the linear stability of the Stokes wave solution, enhances rogue wave formation, and leads to permanent downshift in the spectral peak
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Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-29 Peter A. Clarkson, Clare Dunning
In this paper, rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalized Laguerre polynomials, which are the main subject of this paper, and the other in terms of the generalized Umemura polynomials. Both the generalized Laguerre polynomials and the generalized Umemura polynomials
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Exploring the interplay between memory effects and vesicle dynamics: A five-dimensional analysis using rigid sphere models and mapping techniques Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-20 E. Azroul, G. Diki, M. Guedda
The memory effect in vesicle dynamics refers to the persistence of shape changes in lipid vesicles, a type of lipid bilayer membrane that mimics some features of real cells, particularly red blood cells (RBCs). To study this effect, a fractional rigid sphere model in five dimensions has been investigated, which maps the dynamics of a vesicle using the Caputo operator. This model provides new insights
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Symmetries of the DΔmKP hierarchy and their continuum limits Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-16 Jin Liu, Da-jun Zhang, Xuehui Zhao
In the recent paper [Stud. App. Math. 147 (2021), 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev–Petviashvili (DΔmKP) hierarchy converts the DΔmKP system to the relativistic Toda spectral problem and its hierarchy. In this paper, we introduce a new formulation of independent variables in the squared eigenfunction symmetry constraint, under which the
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Korteweg–de Vries waves in peridynamical media Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-13 Michael Herrmann, Katia Kleine
We consider a one-dimensional peridynamical medium and show the existence of solitary waves with small amplitudes and long wavelength. Our proof uses nonlinear Bochner integral operators and characterizes their asymptotic properties in a singular scaling limit.
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Spatiotemporal propagation of a time-periodic reaction–diffusion SI epidemic model with treatment Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-11 Shuang-Ming Wang, Liang Zhang
This work is concerned with the spatiotemporal propagation phenomena for a time-periodic reaction-diffusion susceptible-infectious (SI) epidemic model with treatment in terms of the asymptotic speed of spread and periodic traveling waves. First, the asymptotic speed of spread c∗$c^*$ is characterized and the spreading properties of the model are analyzed by combining the periodic principal eigenvalue
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Spatial propagation of a lattice predation–competition system with one predator and two preys in shifting habitats Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-05 Jun-Feng Li, Jia-Bing Wang
This paper deals with a discrete diffusive predator–prey system involving two competing preys and one predator in a shifting habitat induced by the climate change. By applying Schauder's fixed-point theorem on various invariant cones via constructing several pairs of generalized super- and subsolutions, we establish four different types of supercritical and critical forced extinction waves, which describe
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Dynamical analysis of a degenerate and time delayed virus infection model with spatial heterogeneity Stud. Appl. Math. (IF 2.7) Pub Date : 2023-10-04 Yu Yang, Jing Chen, Lan Zou
This paper is concerned with a degenerate and time delayed virus infection model with spatial heterogeneity and general incidence. The well-posedness of the system, including global existence, uniqueness, and ultimately boundedness of the solutions, as well as the existence of a global attractor, is discussed. The basic reproduction number R0$\mathcal {R}_0$ is defined and a characterization of R0$\mathcal
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Oscillations in three-reaction quadratic mass-action systems Stud. Appl. Math. (IF 2.7) Pub Date : 2023-09-21 Murad Banaji, Balázs Boros, Josef Hofbauer
It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the
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Some exact and approximate solutions to a generalized Maxwell–Cattaneo equation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-09-12 Isom H. Herron, Ronald E. Mickens
The simple heat conduction equation in one-space dimension does not have the property of a finite speed for information transfer. A partial resolution of this difficulty can be obtained within the context of heat conduction by the introduction of a partial differential equation (PDE) called the Maxwell–Cattaneo (M-C) equation, elsewhere called the damped wave equation, a special case of the telegraph
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Local well-posedness of the higher-order nonlinear Schrödinger equation on the half-line: Single-boundary condition case Stud. Appl. Math. (IF 2.7) Pub Date : 2023-09-11 Aykut Alkın, Dionyssios Mantzavinos, Türker Özsarı
We establish local well-posedness in the sense of Hadamard for a certain third-order nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higher-order nonlinear Schrödinger equation, formulated on the half-line {x>0}$\lbrace x>0\rbrace$. We consider the scenario of associated coefficients such that only one boundary condition is required and hence assume
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Geometrical correspondence of the Miura transformation induced from affine Kac–Moody algebras Stud. Appl. Math. (IF 2.7) Pub Date : 2023-09-09 Changzheng Qu, Zhiwei Wu
The Miura transformation plays a crucial role in the study of integrable systems. There have been various extensions of the Miura transformation, which have been used to relate different kinds of integrable equations and to classify the bi-Hamiltonian structures. In this paper, we are mainly concerned with the geometric aspects of the Miura transformation. The generalized Miura transformations from
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Degenerate Cauchy–Goursat problem for 2-D steady isentropic Euler system with van der Waals gas Stud. Appl. Math. (IF 2.7) Pub Date : 2023-09-04 H. Srivastava, M. Zafar
This study concerns with the existence–uniqueness of local classical sonic-supersonic solution to a degenerate Cauchy–Goursat problem that arises in transonic phenomena. The flow is governed by 2-D steady isentropic Euler system with a polytropic van der Waals gas. The idea of characteristic decomposition has been used to convert the Euler system into a new system involving the angle variables ( 𝛩
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A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-31 Fabio A. C. C. Chalub, Antonio Gómez-Corral, Martín López-García, Fátima Palacios-Rodríguez
Ordinary differential equation models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital, this is an extremely restrictive assumption as typically a hospital ward has a few dozen, or even fewer, patients. This work reframes a well-known model used in the study of the spread of antibiotic-resistant bacteria in hospitals, to
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Rogue waves arising on the standing periodic waves in the Ablowitz–Ladik equation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-27 Jinbing Chen, Dmitry E. Pelinovsky
We study the standing periodic waves in the semidiscrete integrable system modeled by the Ablowitz–Ladik (AL) equation. We have related the stability spectrum to the Lax spectrum by separating the variables and by finding the characteristic polynomial for the standing periodic waves. We have also obtained rogue waves on the background of the modulationally unstable standing periodic waves by using
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Existence of global solutions to the nonlocal Schrödinger equation on the line Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-23 Yi Zhao, Engui Fan
We address the existence of global solutions to the Cauchy problem for the integrable nonlocal nonlinear Schrödinger (nonlocal NLS) equation under the initial data q0(x)∈H1,1(R)$q_0(x)\in H^{1,1}(\mathbb {R})$ with the L1(R)$L^1(\mathbb {R})$ small-norm. The nonlocal NLS equation was first introduced by Ablowitz and Musslimani as a new nonlocal reduction of the well-known Ablowitz–Kaup–Newell–Segur
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Hölder stability and uniqueness for the mean field games system via Carleman estimates Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-17 Michael V. Klibanov, Jingzhi Li, Hongyu Liu
We are concerned with the mathematical study of the mean field games system (MFGS). In the conventional setup, the MFGS is a system of two coupled nonlinear parabolic partial differential equation (PDE)s of the second order in a backward–forward manner, namely, one terminal and one initial condition are prescribed, respectively, for the value function and the population density . In this paper, we
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Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-17 Rebecca M. Crossley, Philip K. Maini, Tommaso Lorenzi, Ruth E. Baker
Many reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of
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Miura transformation for the “good” Boussinesq equation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-15 C. Charlier, J. Lenells
It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation
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The KP limit of a reduced quantum Euler–Poisson equation Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-14 Huimin Liu, Xueke Pu
In this paper, we consider the derivation of the Kadomtsev–Petviashvili (KP) equation for cold ion-acoustic wave in the long wavelength limit of a two-dimensional reduced quantum Euler–Poisson system under different scalings for varying directions in the Gardner–Morikawa transform. It is shown that the types of the KP equation depend on the scaled quantum parameter H > 0 $H>0$ . The KP-I is derived
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Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena Stud. Appl. Math. (IF 2.7) Pub Date : 2023-08-10 Tsvetana Stoyanova
In this paper we study the integrability of the Hamiltonian system associated with the fourth Painlevé equation. We prove that one two-parametric family of this Hamiltonian system is not integrable in the sense of the Liouville–Arnold theorem. Computing explicitly the Stokes matrices and the formal invariants of the second variational equations, we deduce that the connected component of the unit element