Modification of the Clarkson--Kruskal Direct Method for a Coupled System
Modification of the Clarkson-Kruskal Direct Method for a Coupled System

A new idea is put forward to modify the Clarkson--Kruskal (CK) direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.