Soliton Solutions And Applications For Some Nonlinear Different Equations

Based on the soliton theory, this paper mainly studies some nonlinear evolution equations with physical background by using the F-expansion method, extend Tanhmethod and the improved truncated expansion method. With the modern computer technique, we find their new soliton solutions and other exact solutions.The content of this paper is composed of four chapters.In the first part of this paper, we mainly introduce the background, the status of recent researches and the tendency of development of nonlinear different evolution equations and soliton solutions. We also introduce some basic notions on oscillation. In addition, we briefly introduce the research content, the structure of this paper and the research conclusion.In the second part of this paper, we firstly consider the Schrodinger-KdV equations:These equations have broad applications in plasma physics, such as; it can be used to describe Laugmuir wave and electromagnetic wave and so on. In this part, The F-expansion method is used to solve the coupled Schrodinger--KdV equations with computerized symbolic computation .By this method, we acquire many Jacobian ellipse functions solutions. These solutions can degenerate trigonometric functions solutions and soliton solutions in limit instance.In the third part of this paper, we use extend Tanh-method to discuss the Hirota-Satsuna system of coupled KdV equations (HSKdVs):Where a(x,t),b(x,t),c(x,t),d(x,t),e(x,t)are all nonzero function with the variable of x and t. The coupled equations are important in many fields, such as nonlinear optics, fluid dynamics, supersymmetry and so on. In fluid dynamics, they can describe interactions of two long waves with different dispersion relations. We obtained the exact analytic solutions for the variable-coefficient Hirota-Satsuna system of coupled KdV equations include Jacobian ellipse functions and trigonometric functions via the restriction of the coefficientIn the fourth part of this paper, we give a new improved truncated expansion method. In order to introduce how to use this method; we discussed the Burgers equation and the approximate equation for long water waves:1.Burgers equation:u_t+2uu_x+u_xx=0 (3)2. The approximate equation for long water waves:By using symbolic software like Mathematica, we obtain numerical simulation pictures of the approximate equation for long water waves.Fifth chapter is this article conclusion part, mainly the work which does to the full text carries on the summary.