Research On Meromorphic Solutions Of Some Algebraic Differential Equations

In this thesis, we mainly consider a class of algebraic differential equation: the Real Cubic Swift-Hohenberg euqation where α, C are arbitrary constants.The main work of this thesis is to research meromorphic solutions expression of algebraic differential equation mentioned above. In the first chapter we intro-duce the thesis’ research work, background, research purpose and so on. In the second chapter we outline the basic knowledge of algebraic differential equations and introduce the method given by Kudryashov to find meromorphic solutions of algebraic differential equations. In the third chapter we introduce the meromorphic solutions of some algebraic differential equations. In the forth chapter we mainly discuss the solutions expression of the Real Cubic Swift-Hohenberg euqation, all meromorphic solutions (i.e., elliptic function solutions, rational function solutions, rational function solutions of one exponential eαz) are obtained by combining sym-bolic computation software Maple and the method given by Kudryashov. Some unsolved problems are given in the last chapter.