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Lie symmetry analysis, optimal system and exact solutions for a NLPDE from the reduced quasi-classical self-dual Yang–Mills equation

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Abstract

In this paper, the classical Lie group method is employed to obtain exact solutions for a nonlinear partial differential equation (NLPDE) derived from the reduced quasi-classical self-dual Yang–Mills equation. An infinite-dimensional Lie algebra is obtained, and by utilizing a seven-dimensional subspace of this algebra, the commutator table and adjoint representation table are constructed. These tables facilitate the construction of the optimal system for the equation, leading to precise solutions. The obtained solutions are presented graphically, accompanied by a suitable analysis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 12201325, 12235007).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, China

    Xianglong Zhang & Bao Wang

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  1. Xianglong Zhang
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  2. Bao Wang
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Correspondence to Bao Wang.

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Zhang, X., Wang, B. Lie symmetry analysis, optimal system and exact solutions for a NLPDE from the reduced quasi-classical self-dual Yang–Mills equation. Eur. Phys. J. Plus 139, 329 (2024). https://doi.org/10.1140/epjp/s13360-024-05131-0

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