Studies On Auxiliary Equation Methods For Solving Several Nonlinear Evolution Equations

An important research area of Soliton theory is to solve the exact solutions ofnonlinear evolution equations. Auxiliary equation method as a kind of effectivemethods which used to solve the exact solutions of nonlinear evolution equations, and ithas been widely used in recent years.This paper mainly studies auxiliary equation method to solve some problems onnonlinear evolution equations.The part of introduction, which introduces the history of several importanthistorical events of soliton theory, and the history and prospects of auxiliary equationmethod.The overview of several common auxiliary equation methods, including Riccatiequation method, F-expansion method, the G’/G-expansion method and Fansub-equation method. And it introduces and analyzes the process of auxiliary equationmethod to solve nonlinear evolution equations, and then illustrates some of theadvantages of auxiliary equation method.Expands to application of auxiliary equation method on nonlinear evolutionequations, and raises modified Fan sub-equation to solve high dimensional nonlinearevolutions equations. We use the modified method to solve the (3+1)-dimensionalJimbo-Miwa equation and the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyamaequation, and get some new solutions.We give a new application of the auxiliary equation method, in which the usedauxiliary equation. As a result, we obtain many solutions of the (2+1)-dimensionalKonopelchenko–Dubrovsky equation.