doi:10.16186/j.cnki.1673-9787.2020090031

Received:2020/09/06

Revised:2021/01/13

Published:2021/09/15

New exact solutions for the general KdV-mKdV equation

GUOChunxiao 1, GUOYanfeng 2,3

1.Department of Mathematics， China University of Mining and Technology （ Beijing） ， Beijing  100083 ， China;2.School of Science， Guangxi University of Science and Technology， Liuzhou  545006 ， Guangxi， China;3.School of Mathematics and Physics， China University of Geosciences， Wuhan  430074，Hubei，China

Abstract:In order to obtain some new exact solutions of the general KdV-mKdV equation ， combining with the new auxiliary ordinary equations and the homogeneous balance theory ， improved G'/G-expansion method was pro-posed and was applied to study new solutions and theory of rogue wave. The solutions were constructed by hyperbolic ， trigonometric and rational function forms for the general KdV-mKdV equation ， which included a part of solutions of mKdV equation in particular. According to the relationship between these parameters in the un-determined form of the solution ， the formation mechanism of the corresponding rogue waves was explained by the graph of the new solutions in detail. It was important to explain the rogue waves phenomenon in nature.

Key words:general KdV-mKdV equation;improved G'/G-expansion method;homogeneous balance;new exact solutions;rogue wave

 一类广义KdV-mKdV方程新的精确解_郭春晓.pdf