Some exact solutions to the generalized Korteweg–de Vries equation and the system of shallow water wave equations

Abstract

In this paper, we establish exact solutions for nonlinear evolution equations in mathematical physics. The exp-transform method is proposed to seek solitary solutions, periodic solutions and compaction-like solutions of nonlinear differential equations. The generalized KdV equation and the system of the shallow water wave equation are chosen to illustrate the effectiveness and convenience of the method.