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The Interactions of N‐Soliton Solutions for the Generalized (2 + 1)‐Dimensional Variable‐Coefficient Fifth‐Order KdV Equation

Author

Listed:
  • Xiangrong Wang
  • Xiaoen Zhang
  • Yong Zhang
  • Huanhe Dong

Abstract

A generalized (2 + 1)‐dimensional variable‐coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity‐capillary waves better than the (1 + 1)‐dimensional KdV equation. The N‐soliton solutions of the (2 + 1)‐dimensional variable‐coefficient fifth‐order KdV equation are obtained via the Bell‐polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell‐polynomial and the period wave solutions are given by applying the Riemann theta function method.

Suggested Citation

  • Xiangrong Wang & Xiaoen Zhang & Yong Zhang & Huanhe Dong, 2015. "The Interactions of N‐Soliton Solutions for the Generalized (2 + 1)‐Dimensional Variable‐Coefficient Fifth‐Order KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:904671
    DOI: 10.1155/2015/904671
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    References listed on IDEAS

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    1. Huanhe Dong & Yanfeng Zhang & Yongfeng Zhang & Baoshu Yin, 2014. "Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, July.
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