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Painlevé analysis, group classification and exact solutions to the nonlinear wave equations

Author

Listed:
  • Hanze Liu

    (School of Mathematical Sciences, Liaocheng University)

  • Cheng-Lin Bai

    (School of Physics Science and Information Engineering, Liaocheng University)

  • Xiangpeng Xin

    (School of Mathematical Sciences, Liaocheng University)

Abstract

This paper is concerned with the general regular long-wave (RLW) types of equations. By the combination of Painlevé analysis and Lie group classification method, the conditional Painlevé property (PP) and Bäcklund transformations (BTs) of the nonlinear wave equations are provided under some conditions. Then, all of the point symmetries of the nonlinear RLW types of equations are obtained, the exact solutions to the equations are investigated. Particularly, some explicit solutions are provided by the special function and Φ-expansion method. Graphical abstract

Suggested Citation

  • Hanze Liu & Cheng-Lin Bai & Xiangpeng Xin, 2020. "Painlevé analysis, group classification and exact solutions to the nonlinear wave equations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(2), pages 1-8, February.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:2:d:10.1140_epjb_e2020-100402-6
    DOI: 10.1140/epjb/e2020-100402-6
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    Keywords

    Statistical and Nonlinear Physics;

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