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Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics

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  • Khaled A. Gepreel

Abstract

We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein‐Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function‐like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

Suggested Citation

  • Khaled A. Gepreel, 2013. "Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:258396
    DOI: 10.1155/2013/258396
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    References listed on IDEAS

    as
    1. Yong Chen & Zheng Yu, 2003. "Generalized Extended Tanh-Function Method To Construct New Explicit Exact Solutions For The Approximate Equations For Long Water Waves," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 601-611.
    2. Khaled A. Gepreel & A. R. Shehata, 2012. "Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, March.
    3. Zhenya Yan, 2003. "A REDUCTIONmKdVMETHOD WITH SYMBOLIC COMPUTATION TO CONSTRUCT NEW DOUBLY-PERIODIC SOLUTIONS FOR NONLINEAR WAVE EQUATIONS," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 661-672.
    4. Khaled A. Gepreel & A. R. Shehata, 2012. "Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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