Generalized Riccati equation expansion method and its application to the (2+1)-dimensional Boussinesq equation

作者：Chen Y^*; Li B; Zhang HQ

来源：International Journal of Modern Physics C, 2003, 14(4): 471-482.

DOI：10.1142/S0129183103004668

• Riccati equation
• computerized symbolic system
• (2+1)-dimensional Boussinesq equation
• soliton-like solutions

Based on the computerized symbolic system Maple and 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 ansatz. 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.

• 出版日期2003-5
• 单位大连理工大学