Travelling Wave Solutions For Generalized Dullin-gottwald-holm Equation And K*(4,1) Equation

The nonlinear phenomenon is very concerned about the study of many fields ofnatural sciences. With the development of nonlinear science, solving nonlinearequations has become an important research topic in the field of nonlinear science.Recent decades, many researchers have studied nonlinear equations by using variousmethods, such as inverse scattering method, Hirota bilinear method, Lie groupmethod, homogenous balance method, bifurcation method of dynamic systems,hyperbolic function method, Fan-expansion method and so on. Tt is too difficulty tosolving nonlinear differential equations, and there is no unified method can beemployed to handle all types of nonlinear differential equation. Therefore, it is ofgreat theoretical significance and application value for solving the exact travelingwave solutions of nonlinear partial differential equations.On the basis of previous studies of solving nonlinear differential equations, thispaper studied the generalized Dullin-Gottwald-Holm equation and the K*4,1equation by using the travelling wave transformation、the homogeneous boundarycondition、the theory of planar dynamical system. The parametric conditions ofexistence of the soliton solutions are given by using the phase portrait analyticaltechnique and numerical graph.The structure of the paper is organized as follows:The first chapter, we mainly talk about the historical background, researchdevelopments and research significance of the generalized Dullin-Gottwald-Holmequation and KdV equation.The second chapter, we introduce some basic theories and methods related tothis 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 theK*(4,1)equation underdifferent parametric conditions.The fifth chapter is a summary of the whole paper.