GENERALIZED RICCATI EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE (2+1)-DIMENSIONAL BOUSSINESQ EQUATION

Yong Chen (), Biao Li () and Hongqing Zhang
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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

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 04, 471-482

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.

Keywords: Riccati equation; computerized symbolic system; (2+1)-dimensional Boussinesq equation; soliton-like solutions (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103004668

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