Similarity Reduction and Exact Solutions of a Boussinesq-like Equation

Abstract

The similarity reduction and similarity solutions of a Boussinesq-like equation are obtained by means of Clarkson and Kruskal (CK) direct method. By using Lie symmetry method, we also obtain the similarity reduction and group invariant solutions of the model. Further, we compare the results obtained by the CK direct method and Lie symmetry method, and we demonstrate the connection of the two methods.