广义耦合Hirota-Satsuma KdV方程组的对称约化和精确解

Symmetry Reduction and Exact Solutions of the Generalized Coupled Hirota-Satsuma KdV System

利用修正的CK直接方法,得到广义耦合Hirota-Satsuma KdV方程组的经典李点对称,并利用对称得到该方程的一些相似约化和新的精确解,同时,建立了该方程组的新、旧解之间的关系,从而推广了本文所得的新解.

Applying the modified Clarkson-Kruskal direct method, the classical Lie point symmetry of the generalized coupled Hirota- Satsuma KdV system was derived. The similarity reduction and exact solutions of the system were obtained by applying the given Lie symmetry. At the same time, the relationship between the old and new solutions was set up, which generalized the new solutions.