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Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method

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  • Khani, F.

Abstract

In this paper, we use the Exp-function method to construct the generalized solitary wave solutions of the generalized (1+1)-dimensional and the generalized (2+1)-dimensional Ito equations. These equations play a very important role in mathematical physics and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The results show the reliability and efficiency of the proposed method. Finally, some new solitonary wave solutions are obtained.

Suggested Citation

  • Khani, F., 2009. "Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2128-2134.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:2128-2134
    DOI: 10.1016/j.chaos.2008.08.023
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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Bai, Cheng-Lin & Zhao, Hong, 2006. "Generalized extended tanh-function method and its application," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1026-1035.
    3. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    4. Zhao, Xiqiang & Wang, Limin & Sun, Weijun, 2006. "The repeated homogeneous balance method and its applications to nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 448-453.
    5. Zhang, Sheng, 2008. "Application of Exp-function method to high-dimensional nonlinear evolution equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 270-276.
    6. Darvishi, M.T. & Khani, F., 2009. "Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2484-2490.
    7. Yomba, Emmanuel, 2005. "The modified extended Fan’s sub-equation method and its application to (2+1)-dimensional dispersive long wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 785-794.
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