The Traveling Wave Solutions Of Lotka-Volterra Diffusion System And The Study Of Asymptotic Behavior

Lotka-Volterra system is one of the most important systems in mathematical biology areas. Some scholars proved the existence of traveling wave solutions after1982, the construction of exact traveling wave solutions of Lotka;-Volterra system becomes a significant issue.The traveling wave solutions provides a powerful tool for the study of the dynamic behavior.The main results of this paper obtain that:1.we will use the tanh-function expansion method and the G’/G expansion method to establish the exact traveling wave solutions for the Lotka-Volterra diffusion system.A series of new exact solutions are obtained which include rational function solutions, trigonometric function solutions and hyperbolic function solutions.2. We will discuss whether its corresponding asymptotic behavior exist or not and their condi-tions.3.Last, respectively, two kinds of function expansion method are used to solve the non fully symmetrical Lotka-Volterra diffusion system, and discuss their asymptotic behavior.