形变映射法求Boussinesq方程的显式精确行波解

Searching for explicit and exact traveling wave solutions of Boussinesq equation by means of deformation mapping method

利用形变映射法 ,建立Boussinesq方程与三次非线性Klein -Gordon(NKG)方程一类特殊类型解的代数变换关系 .根据该关系以及NKG方程的已知解 ,获得Boussinesq方程系统丰富的显式精确行波解 ,包括孤波解 ,周期波解 ,雅可比椭圆函数解和其他精确解 .

Deformation mapping method is applied to obtain exact solutions of Boussinesq equation. A simple algebraic transformation relation of a special type of solution between the Boussinesq equation and the cubic nonlinear Klein-Gordon (NKG) equation is established. With the aid of this relation and known solutions of the NKG equation, abundant explicit and exact traveling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and others exact solutions, are obtained.