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Traveling Wave Solutions and Infinite-Dimensional Linear Spaces of Multiwave Solutions to Jimbo-Miwa Equation

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  • Lijun Zhang
  • C. M. Khalique

Abstract

The traveling wave solutions and multiwave solutions to (3 + 1)-dimensional Jimbo-Miwa equation are investigated in this paper. As a result, besides the exact bounded solitary wave solutions, we obtain the existence of two families of bounded periodic traveling wave solutions and their implicit formulas by analysis of phase portrait of the corresponding traveling wave system. We derive the exact 2-wave solutions and two families of arbitrary finite N -wave solutions by studying the linear space of its Hirota bilinear equation, which confirms that the (3 + 1)-dimensional Jimbo-Miwa equation admits multiwave solutions of any order and is completely integrable.

Suggested Citation

  • Lijun Zhang & C. M. Khalique, 2014. "Traveling Wave Solutions and Infinite-Dimensional Linear Spaces of Multiwave Solutions to Jimbo-Miwa Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    • Handle: RePEc:hin:jnlaaa:963852
    DOI: 10.1155/2014/963852
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    Cited by:

    1. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.

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