摘要

This paper presents some new exact solutions which contain soliton solutions, breather solutions and two types of rational solutions for the variable-coefficientmodified Korteweg-de Vries equation, with the help of the multivariate transformation technique. Furthermore, based on these new soliton solutions, breather solutions and rational solutions, we discuss their non-linear dynamics properties. We also show the graphic illustrations of these solutions which can help us better understand the evolution of solution waves.