The Study Of The Solution To A Class Of Shallow Water Wave Equation

From a differential dynamical point of view the paper studies the properties of the traving wave solution to shallow water wave equation,emphasizing in doing research to the traving wave solution of Generalized Hyperelastic-Rod wave equation. Firstly, the paper transfer the partial differential equation into ordinary differential equation, discusses the necessary condition of the existence of traving wave solution of this equation, then studies the existence of traveling wave solution to this eqution when g(u) is inpolynomial and exponential conditions. At last, via phase space (φ,η), equilibrium point and trajectory of this equation are discussed and the existence of limit cycles is studied.On the other hand, This paper studies the solitary wave of the combined Kdv-mkdv equation. This paper uses the relation between solitary wave of the combined Kdv -mkdv equation and homoclinic orbit of autonomous system (u,y) and the bifurcation theory of dynamical system to study the homoclinic orbits of on all parametric conditions, and then investigates the existence of solitary waves of the combined Kdv and mkdv equation.In the end, the papermakes the study to solitary wave solutions and periodic wave solutions for a (2+1)-Dimensional Burgers equation. The F-expansion method is extended, in which the terms with inverse powers of F are appeared, in which F=F(ξ) be a solution of Riccati eqation. By means of this method and Mathematica, some solitary wave solutions and periodic wave solutions for a (2+1)-Dimensional Burgers equation have been gained.