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Exact solutions for a class of nonlinear evolution equations: A unified ansätze approach

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  • Khuri, S.A.

Abstract

In this paper, we propose a modified generalized transformation for constructing analytic solutions to nonlinear differential equations. This improved unified ansätze is utilized to acquire exact solutions that are general solutions of simpler equations that are either integrable or possess special solutions. The ansätze is constructed via the choice of an integrable differential operator or a basis set of functions. The technique is implemented to obtain several families of exact solutions for a class of nonlinear evolution equations with nonlinear term of any order. In particular, the Klein–Gordon, the Sine–Gordon and Landau–Ginburg–Higgs equations are chosen as examples to illustrate the method.

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  • Khuri, S.A., 2008. "Exact solutions for a class of nonlinear evolution equations: A unified ansätze approach," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1181-1188.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1181-1188
    DOI: 10.1016/j.chaos.2006.09.066
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    References listed on IDEAS

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    1. Khuri, S.A., 2005. "Soliton and periodic solutions for higher order wave equations of KdV type (I)," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 25-32.
    2. Yong Chen & Biao Li & Hong-Qing Zhang, 2003. "Exact Traveling Wave Solutions For Some Nonlinear Evolution Equations With Nonlinear Terms Of Any Order," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 99-112.
    3. Khuri, S.A., 2005. "New ansätz for obtaining wave solutions of the generalized Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 705-710.
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    Cited by:

    1. Abdul-Majid Wazwaz & Ma’mon Abu Hammad & Ali O. Al-Ghamdi & Mansoor H. Alshehri & Samir A. El-Tantawy, 2023. "New (3+1)-Dimensional Kadomtsev–Petviashvili–Sawada– Kotera–Ramani Equation: Multiple-Soliton and Lump Solutions," Mathematics, MDPI, vol. 11(15), pages 1-11, August.

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    1. Khuri, S.A., 2007. "Traveling wave solutions for nonlinear differential equations: A unified ansätze approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 252-258.
    2. Abdul-Majid Wazwaz & Ma’mon Abu Hammad & Ali O. Al-Ghamdi & Mansoor H. Alshehri & Samir A. El-Tantawy, 2023. "New (3+1)-Dimensional Kadomtsev–Petviashvili–Sawada– Kotera–Ramani Equation: Multiple-Soliton and Lump Solutions," Mathematics, MDPI, vol. 11(15), pages 1-11, August.

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