Similarity and conditional similarity reductions of a \((2+1)\)-dimensional KdV equation via a direct method (Q2731839)

The authors try to find similarity solutions of a nonlinear physical equation, the conditional similarity reductions, by the direct method with a suitable modification which cannot be obtained by the nonclassical Lie group approach. The usual Clarkson and Kruskal method to obtain some two dimensional similarity solutions (method) is used. The method is modified to obtain some conditional similarity reductions. Nontriviality of the method is explained by listing some special solutions of the conditional similarity reductions.