The Soliton Solutions Of A Class Of Nonlinear Dispersive Wave Equation

Nonlinear Science,which has solution theory,fractal and chaos as its main parts,is the subject of studying the common futures of nonlinearity. Nonlinearity is universal and important.Most nonlinear problem can be described by nonlinear equations,which generally includes nonlinear.How to obtain the exact solutions of nonlinear equations is of vital importance to study of the corresponding problem.The key problem in soliton theory is to get solutions of the nonlinear evolution equations, including exact ones or numerical ones.During the past 50 years or so, the scientists have created various ingenious methods to construct exact solutions,especially soliton solutions of nonlinear equations.In this paper,we should used above methods to study nonlinear dispersive wave equation.In chapter 1 and chapter 2,we introduce the study background,study development and significance of nonlinear wave equation and soliton theory.The methods known up to today for solving the nonlinear wave equation are summarized and analyzed.Then the concerned concepts and theories which used in this paper are introduced.In the third chapter,the qualitative analysis methods of dynamical system are used to investigate the soliton solutions of the generalizedγ-CH equation.Using the way of the phase portrait bifurcation analysis and mathematical software,we obtain the soliton solutions by the solutions corresponding to the homoclinic orbit, heteroclinic orbit and the periodic orbit.However we give the conditions of there are exist smooth periodic wave solutions,smooth soliton wave solutions,periodic cusp solutions,kink-like wave solutions,antikink-like solutions.And exact explicit parametric representations of periodic cusp solutions and soliton cusp wave solutions are given and the numerical simulation is made.In the forth chapter,using the way of the phase portrait bifurcation analysis,we study kink-like wave solutions and antikink-like solutions of the F-W equation.The exact explicit parametric representations of those solutions are obtained and the numerical simulation is made.