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The Rational Solutions and Quasi‐Periodic Wave Solutions as well as Interactions of N‐Soliton Solutions for 3 + 1 Dimensional Jimbo‐Miwa Equation

Author

Listed:
  • Hongwei Yang
  • Yong Zhang
  • Xiaoen Zhang
  • Xin Chen
  • Zhenhua Xu

Abstract

The exact rational solutions, quasi‐periodic wave solutions, and N‐soliton solutions of 3 + 1 dimensional Jimbo‐Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant solution which is a special form of the N‐soliton solutions. At last, the interactions of the solitons are shown with the aid of N‐soliton solutions.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:7241625
    DOI: 10.1155/2016/7241625
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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).
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