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A REDUCTIONmKdVMETHOD WITH SYMBOLIC COMPUTATION TO CONSTRUCT NEW DOUBLY-PERIODIC SOLUTIONS FOR NONLINEAR WAVE EQUATIONS

Author

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  • ZHENYA YAN

    (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China)

Abstract

Firstly twenty-four types of doubly-periodic solutions of the reductionmKdVequation are given. Secondly based on the reductionmKdVequation and its solutions, a systemic transformation method (called the reductionmKdVmethod) is developed to construct new doubly-periodic solutions of nonlinear equations. Thirdly with the aid of symbolic computation, we choose theKdVequation, the coupled variant Boussinesq equation and the cubic nonlinear Schrödinger equation to illustrate our method. As a result many types of solutions are obtained. These show that this method is simple and powerful to obtain more exact solutions including doubly-periodic solutions, soliton solutions and singly-periodic solutions to a wide class of nonlinear wave equations. Finally we further extended the method to a general form.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:05:n:s0129183103004814
    DOI: 10.1142/S0129183103004814
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