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The novel solutions of auxiliary equation and their application to the (2+1)-dimensional Burgers equations

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  • Wang, Deng-Shan
  • Li, Hong-Bo
  • Wang, Jike

Abstract

The present paper deals with families of non-trivial novel solutions of the general elliptic equation ϕ′2(ξ)=ddξϕ2=a0+a1ϕ+a2ϕ2+a3ϕ3+a4ϕ4. Based on these novel solutions, a direct and generalized algebraic algorithm is described to construct the new non-travelling wave solutions of systems of nonlinear partial differential equations (NLPDEs). Subsequently, a series of important non-travelling wave solutions of the (2+1)-dimensional Burgers equations are obtained.

Suggested Citation

  • Wang, Deng-Shan & Li, Hong-Bo & Wang, Jike, 2008. "The novel solutions of auxiliary equation and their application to the (2+1)-dimensional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 374-382.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:374-382
    DOI: 10.1016/j.chaos.2006.11.025
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    References listed on IDEAS

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    1. Wang, Qi & Chen, Yong & Zhang, Hongqing, 2005. "A new Riccati equation rational expansion method and its application to (2+1)-dimensional Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1019-1028.
    2. Dengshan Wang & Hong-Qing Zhang, 2005. "Auto-Bäcklund Transformation And New Exact Solutions Of The(2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 393-412.
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    4. Li, Xiaoyan & Yang, Sen & Wang, Mingliang, 2005. "The periodic wave solutions for the (3+1)-dimensional Klein–Gordon–Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 629-636.
    5. Chen, Yong & Wang, Qi & Li, Biao, 2005. "Elliptic equation rational expansion method and new exact travelling solutions for Whitham–Broer–Kaup equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 231-246.
    6. Yomba, Emmanuel, 2006. "The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer–Kaup–Kupershmidt equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 187-196.
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