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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:963852
    DOI: 10.1155/2014/963852
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    References listed on IDEAS

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    1. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
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    1. Hongwei Yang & Yong Zhang & Xiaoen Zhang & Xin Chen & Zhenhua Xu, 2016. "The Rational Solutions and Quasi‐Periodic Wave Solutions as well as Interactions of N‐Soliton Solutions for 3 + 1 Dimensional Jimbo‐Miwa Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).

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