一类变系数偏微分方程的精确解的求法及其计算机机械化实现

The variable-coe?cient partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain variable-coe?cient partial differential equations, the aux-iliary elliptic-like equation method is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain variable-coe?cient partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the Kadomtsev-Petviashvili equation for an example, not only the effectiveness of the algorithm is demonstrated, but many new solutions are worked out, including dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions, which may be useful for depicting nonlinear physical phenomena.

New Exact Solutions to a Category of Variable-coefficient PDEs and Computerized Mechanization

The variable-coe?cient partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain variable-coe?cient partial differential equations, the aux-iliary elliptic-like equation method is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain variable-coe?cient partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the Kadomtsev-Petviashvili equation for an example, not only the effectiveness of the algorithm is demonstrated, but many new solutions are worked out, including dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions, which may be useful for depicting nonlinear physical phenomena.