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The presentation of explicit analytical solutions of a class of nonlinear evolution equations

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  • Jin-Shun, Feng
  • Ming-Pu, Guo
  • Deyou, Yuan

Abstract

In this paper, we introduce a function set Ωm. There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ωm. A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.

Suggested Citation

  • Jin-Shun, Feng & Ming-Pu, Guo & Deyou, Yuan, 2009. "The presentation of explicit analytical solutions of a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2422-2428.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2422-2428
    DOI: 10.1016/j.chaos.2008.09.019
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    References listed on IDEAS

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    1. Wu, Yongyan & Wang, Chun & Liao, Shi-Jun, 2005. "Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1733-1740.
    2. Zhu, Yonggui & Chang, Qianshun & Wu, Shengchang, 2005. "Exact solitary-wave solutions with compact support for the modified KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 365-369.
    3. Wei, Cai-Min & Xia, Zun-Quan & Tian, Nai-Shuo, 2005. "Jacobian elliptic function expansion solutions of nonlinear stochastic equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 551-558.
    4. Wei, Cai-Min & Wang, Jian-Jun, 2008. "Travelling wave solutions to the generalized stochastic KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 733-740.
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