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The Interactions of -Soliton Solutions for the Generalized ( )-Dimensional Variable-Coefficient Fifth-Order KdV Equation

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

Abstract

A generalized ( )-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the ( )-dimensional KdV equation. The -soliton solutions of the ( )-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 ; when , the soliton fusion and fission will happen; when , 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 -Soliton Solutions for the Generalized ( )-Dimensional Variable-Coefficient Fifth-Order KdV Equation," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-11, November.
    • Handle: RePEc:hin:jnlamp:904671
    DOI: 10.1155/2015/904671
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