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Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation

Author

Listed:
  • Lihui Gao

    (School of Science, China University of Mining and Technology, Beijing 100083, China)

  • Chunxiao Guo

    (School of Science, China University of Mining and Technology, Beijing 100083, China)

  • Yanfeng Guo

    (School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China
    School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China)

  • Donglong Li

    (School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China)

Abstract

By the extended ( G ′ G ) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended ( G ′ G ) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rational functions, which reflect different types of solutions for nonlinear waves. Finally, we discuss the effects of these solutions on the formation of rogue waves according to the numerical simulation.

Suggested Citation

  • Lihui Gao & Chunxiao Guo & Yanfeng Guo & Donglong Li, 2022. "Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2522-:d:867061
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