New similarity solutions for the generalized variable-coefficients KdV equation by using symmetry group method

Abstract

In this paper, a generalized variable-coefficients KdV equation (gvcKdV) arising in fluid mechanics, plasma physics and ocean dynamics is investigated by using symmetry group analysis. Two basic generators are determined, and for every generator, the admissible forms of the variable coefficients and the corresponding reduced ordinary differential equations are obtained. Finally, by searching for solutions to those reduced ordinary differential equations, many new exact solutions for the gvcKdV equation have been found.