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Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation

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  • Jingzhu Wu
  • Xiuzhi Xing
  • Xianguo Geng

Abstract

The relations between -operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with -operators of nonlinear equations directly and quickly. Exact periodic wave solution of a (3+1)-dimensional generalized shallow water equation is obtained with the help of the -operators and a general Riemann theta function in terms of the Hirota method, which illustrate that bilinear -operators can provide a method for seeking exact periodic solutions of nonlinear integrable equations. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.

Suggested Citation

  • Jingzhu Wu & Xiuzhi Xing & Xianguo Geng, 2015. "Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-9, September.
    • Handle: RePEc:hin:jnlamp:291804
    DOI: 10.1155/2015/291804
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    Cited by:

    1. Sudao Bilige & Leilei Cui & Xiaomin Wang, 2023. "Superposition Formulas and Evolution Behaviors of Multi-Solutions to the (3+1)-Dimensional Generalized Shallow Water Wave-like Equation," Mathematics, MDPI, vol. 11(8), pages 1-12, April.

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