Explicit exact solutions of some nonlinear evolution equations with their geometric interpretations

摘要

In this paper, the simplest equation method is applied to obtain multiple explicit exact solutions of the combined dispersion equation, the Hirota–Satsuma Korteweg–de Vries system and the generalized Burgers–Huxley equation. These solutions are constructed on the basis of solutions of Bernoulli equation which is used as simplest equation. It is shown that this method is very powerful tool for obtaining exact solutions of a large class of nonlinear partial differential equations. The geometric interpretation for some of these solutions are introduced.