Soliton-like solutions and periodic form solutions for two variable-coefficient evolution equations using symbolic computation

Abstract

Some variable-coefficient generalizations of some nonlinear evolution equations (NLEEs) bear more realistic physical importance. By means of a generalized Riccati equation expansion (GREE) method and a symbolic computation system – Maple – we investigate the variable-coefficient Fisher-type equation and the nearly concentric KdV equation. As a result, rich families of exact analytic solutions for these two equations, including the non-travelling wave’s and coefficient functions’ soliton-like solutions, singular soliton-like solutions, and periodic form solutions, are obtained.