广义Dullin-Gottwald-Holm方程和K(4,1)方程的行波解-基础数学专业论文.docxVIP

Abstract Abstract II II Abstract The nonlinear phenomenon is very concerned about the study of many fields of natural sciences. With the development of nonlinear science, solving nonlinear equations has become an important research topic in the field of nonlinear science. Recent decades, many researchers have studied nonlinear equations by using various methods, such as inverse scattering method, Hirota bilinear method, Lie group method, homogenous balance method, bifurcation method of dynamic systems, hyperbolic function method, Fan-expansion method and so on. Tt is too difficulty to solving nonlinear differential equations, and there is no unified method can be employed to handle all types of nonlinear differential equation. Therefore, it is of great theoretical significance and application value for solving the exact traveling wave solutions of nonlinear partial differential equations. On the basis of previous studies of solving nonlinear differential equations, this paper studied the generalized Dullin-Gottwald-Holm equation and the K * ?4,1? equation by using the travelling wave transformation、the homogeneous boundary condition、the theory of planar dynamical system. The parametric conditions of existence of the soliton solutions are given by using the phase portrait analytical technique and numerical graph. The structure of the paper is organized as follows: The first chapter, we mainly talk about the historical background, research developments and research significance of the generalized Dullin-Gottwald-Holm equation and KdV equation. The second chapter, we introduce some basic theories and methods related to this paper. The third chapter, we discuss the solutions of the generalized Dullin-Gottwald- Holm equation under different parametric conditions. The fourth chapter, we discuss the solutions of the different parametric conditions. The fifth chapter is a summary of the whole paper. K * (4,1) equation under Key words: generalized Dullin-Gottwald-Holm