Exact Solutions To Some Important Nonlinear Evolutionary Equations

Looking for exact solutions to nonlinear partial differential equations (NLPDEs) has long been a major concern for both mathematicians and physicists. These solutions may well describe various phenomena in many fields, so it is wildly used in chemistry, biology, Optical fiber communication, fluid mechanics, plasma physics, quantum field theory. In the paper, we ameliorate to the SUb-ODE method, simplified, enriched and expanded the result we have known. Which has active meaning for us to find new soliton solutions, research the long time dynamic behavior and structure of solitons .At the same time, we classify the structure of solitons, and draw the relevant graphics.In the first chapter, we study the history, current situation and future of our research work, at the same time introduce the main work of this paper.In the second chapter, we introduce some primary conception and denotation relate to this paper, give the definition and befallen mechanism of solitons, discuss the similarities and differences between soliton with solitary wave, classified the solitons which we have known according to the dimension of the space, and draw the relevant graphics.In the third chapter, we ameliorate to the traditional Sub-ODE method, and use this method to research the several kinds of nonlinear evolution equations, and obtain a lot of new significativ solutions . In the fourth chapter, we use a polynomial expansion method with a computerized symbolic computation for solving new periodic wave solutions for nonlinear Equal width wave equation arising in mathematical physics, and obtain many new significativ solutions.In the fifth chapter, the improved projective Riccati method is used for solving Ginzburg-Landau equation; and a lot of envelope wave solutions are successfully obtained.