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Traveling wave solutions for nonlinear differential equations: A unified ansätze approach

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  • Khuri, S.A.

Abstract

The aim of the paper is to introduce a general transformation for constructing analytic solutions for nonlinear differential equations. The main thrust of this alternate approach is to manipulate a unified ansätze to obtain exact solutions that are general solutions of simpler integrable equations. The ansätze is based on either the choice of an integrable differential operator or on a basis set of functions. Trigonometric, hyperbolic, Weierstrass and Jacobi elliptic functions can be used as building blocks for obtaining the exact solutions. The technique is implemented to acquire traveling wave solutions for the KDV–Burgers–Kuramoto equation.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:252-258
    DOI: 10.1016/j.chaos.2005.10.106
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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. 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. Zhang, Huiqun, 2009. "New exact travelling wave solutions of nonlinear evolution equation using a sub-equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 873-881.
    2. Petropoulou, Eugenia N. & Siafarikas, Panayiotis D. & Stabolas, Ioannis D., 2009. "Analytic bounded travelling wave solutions of some nonlinear equations II," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 803-810.

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