Some Exact Solutions For Several Nonlinear Wave Equations

In the field of M athematical Physics,many nonlinear equations have been proposed as mathematical models of natural physical phenomenon.However,due to the complexity of the nonlinear model itself,there is no uniform and universally applicable methods for solving these equations.Therefore,it is still one of the most important research directions in nonlinear science to investigate the traveling wave solutions of nonlinear wave oquations.In this paper,we study the exact solutions of some nonlinear wave equations based on the bifurcation method of dynamical systems and the auxiliary equation method.The main work of this research is as follows.In Chapter 1,we firstly make a brief introduction to the historical background of the Soliton Theory.Furthermore,we generalize some useful methods for solving traveling wave solutions of nonlinear wave equations afterwards.Finally,we summarize the research methods and main work of this dissertation.In Chapter 2,we concern with exact traveling wave solutions of the Boiti-Leon-Pempinelle equation.First,we construct a new Hamiltonian function based on the strue-tural characteristics of the Boiti-Leon-Pempinelle equation.Second,we prove that the equation admit new traveling wave solutions.In Chapter 3,the target of this part is to investigate the exact solutions for the generalized K(m,n)equations and BBM equations with varying coefficients.First,an extended approach is proposed for reducing the order of the equations with higher order nonlinearity.Second,some new exact solutions axe found by auxiliary equation method and symbolic computation.