Abstract

In this study, we investigate a (3+1)-dimensional KP equation, which is widely used to model the behavior of nonlinear waves in plasma physics and fluid mechanics. First, the multi-soliton solutions of the equation are derived using the Hirota bilinear method. Based on the multi-soliton solutions, heterotypic soliton is obtained by setting the partial dispersion coefficient to zero. Under the complex conjugation of the parameters, high-order breather waves are derived. Additionally, the M-lump wave solutions of the equation are derived by applying the long-wave limit. To gain a deeper understanding of its physical dynamics, we conducted numerical simulations to simulate various characteristics of M-lump waves during their propagation, including their peaks, troughs, propagation velocities, and propagation trajectories. Afterward, by combining the long-wave limit with the complex conjugation of the parameters, we discuss three types of multi-wave interaction phenomena described by this equation and illustrate the collision process between waves in graphical form.

中文翻译：

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( $$3+1$$ ) 维 Kadomtsev–Petviashvili 方程的异型孤子、高阶呼吸、M 块波和多波相互作用解的动力学

摘要

在本研究中，我们研究了 (3+1) 维 KP 方程，该方程广泛用于模拟等离子体物理和流体力学中非线性波的行为。首先，使用 Hirota 双线性方法导出方程的多孤子解。在多孤子解的基础上，将部分色散系数设置为零，得到异型孤子。在参数的复杂共轭下，导出了高阶呼吸波。此外，通过应用长波极限导出了方程的M集总波解。为了更深入地了解其物理动力学，我们进行了数值模拟，模拟了M块波在传播过程中的各种特征，包括波峰、波谷、传播速度和传播轨迹。然后，结合长波极限和参数的复杂共轭，讨论了该方程描述的三类多波相互作用现象，并以图形形式说明了波之间的碰撞过程。