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Analytic approximations for the one-loop soliton solution of the Vakhnenko equation

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  • El-Nahhas, A.

Abstract

In this paper, we give an analytic solution for the one-loop soliton solution of the Vakhnenko equation, by the use of the homotopy analysis method and via a fractional basis.

Suggested Citation

  • El-Nahhas, A., 2009. "Analytic approximations for the one-loop soliton solution of the Vakhnenko equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2257-2264.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2257-2264
    DOI: 10.1016/j.chaos.2007.10.013
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    References listed on IDEAS

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    1. Huang, Ding-jiang & Li, De-sheng & Zhang, Hong-qing, 2007. "Explicit N-fold Darboux transformation and multi-soliton solutions for the (1+1)-dimensional higher-order Broer–Kaup system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1677-1685.
    2. Xu, Gui-qiong & Li, Zhi-bin, 2005. "On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1363-1375.
    3. Dai, Zhengde & Li, Shaolin & Dai, Qingyun & Huang, Jian, 2007. "Singular periodic soliton solutions and resonance for the Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1148-1153.
    4. Al-Mdallal, Qasem M. & Syam, Muhammad I., 2007. "Sine–Cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1610-1617.
    5. 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.
    6. Wu, Xiao-Fei & Ge, Hong-Liang & Ma, Zheng-Yi, 2007. "Exact discrete soliton solutions of the nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 940-946.
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