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N-soliton solutions and associated integrability for a novel (2+1)-dimensional generalized KdV equation

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  • Lü, Xing
  • Chen, Si-Jia

Abstract

In this paper, we investigate the integrability of a (2+1)-dimensional generalized KdV equation. In virtue of the Weiss–Tabor–Carnevale method and Kruskal ansatz, this equation can pass the Painlevé test. The truncated Painlevé expansion leads to the Bäcklund transformation and rational solutions. The bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are constructed with the Hirota bilinear method and Bell polynomials. It is proved that the (2+1)-dimensional generalized KdV equation can be regarded as an integrable model in sense of infinite conservation laws. The formula of N-soliton solutions is given and verified with the Hirota condition. The study of integrability provides theoretical guidance for solving equations and gives the possibility of the existence of exact solutions.

Suggested Citation

  • Lü, Xing & Chen, Si-Jia, 2023. "N-soliton solutions and associated integrability for a novel (2+1)-dimensional generalized KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001923
    DOI: 10.1016/j.chaos.2023.113291
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    References listed on IDEAS

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    1. Ma, Wen-Xiu, 2021. "N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 270-279.
    2. Chaudry Masood Khalique, 2013. "Exact Explicit Solutions and Conservation Laws for a Coupled Zakharov-Kuznetsov System," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-5, July.
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