构造非线性发展方程Jacobi椭圆函数精确解的一种方法

在双曲正切函数法、齐次平衡法和辅助方程法的基础上,给出一种双曲函数型辅助方程和函数变换相结合的方法,利用符号计算系统Mathematica构造了正规长波方程和mKdV方程的Jacobi椭圆函数精确解及其退化后的精确孤波解.

Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio

In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation by applying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different coefficients p, q and r in the elliptic equation. Then these solutions are coupled into an auxiliary equation and substituted into the (2+1)-dimensional KDV equation. As a result, a large number of complex Jacobi elliptic function solutions are obtained, and many of them have not been found in other documents. As , some complex solitary solutions are also obtained correspondingly. These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation.

RLW-KdV方程的精确显式行波解

借助计算机符号系统Mathematica,利用Fan代数方法求解RLW-KdV方程。获得了RLW-KdV方程多组精确显式行波解。其中包括孤立波解、周期波解、有理解、Jacobi椭圆函数解。