The Exact Solutions For Three Types Of Nonlinear Partial Differential Equations

Three classes of representative nonlinear partial differential equations are: Klein-Gordon equation, Belousov-Zhabotinskii reaction-diffusion equation, Variant coefficient Boussinesq equations.In order to construct the exact solutions for these equations, the auxiliary differential equation techniques are used ,new exact traveling solutions are obtained.In Chapter 2, by using the method of auxiliary equation of six items, travelling wave solutions of Klein-Gordon equation are constructed.Chapter 3 investigates Belousov-Zhabotinskii reaction-diffusion on system of equations with using generalized auxiliary differential equation method and obtains a series of exact solutions.In Chaper 4, we will employ auxiliary equation method to establish exact solutions of variable coefficient Boussinesq system of equationsMany exact solutions which include periodic solutions, soliton solutions, and exponential solutions are obtained in these three chapters.