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Generalized Riccati Equation Expansion Method And Its Application To The (2+1)-Dimensional Boussinesq Equation

Author

Listed:
  • YONG CHEN

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

  • BIAO LI

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

  • HONGQING ZHANG

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

Abstract

Based on the computerized symbolic systemMapleand a Riccati equation, a new Riccati equation expansion method for constructing nontraveling wave and coefficient functions' soliton-like solutions is presented by a new general ansätz. The proposed method is more powerful than most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method, and generalized hyperbolic-function method. By using the method, we not only successfully recovered the previously known formal solutions but could also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the (2+1)-dimensional Boussinesq equation and obtain rich new families of the exact solutions, including the nontraveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, and triangular functions solutions.

Suggested Citation

  • Yong Chen & Biao Li & Hongqing Zhang, 2003. "Generalized Riccati Equation Expansion Method And Its Application To The (2+1)-Dimensional Boussinesq Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 471-482.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:04:n:s0129183103004668
    DOI: 10.1142/S0129183103004668
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