Exact Solutions To Some Nonlinear Evolution Equations

The soliton theory is an important branch of applied mathematics and mathematical physics. It has important applications in fluid mechanics, classical and quantum fields theories etc. It is one of the most active fields in science. There are many methods to obtain solutions of nonlinear evolution equation in the soliton theory. In this paper, we study multi-dimensional soliton equations and variable coefficient evolution equation.There are six sections in the paper. The first section is an introduction to the development of the evolution equations. In the second section , there are some basic concept of the solitary theory. The third section is an introduction to the method ,which are used。In the fourth section, we use the standard elliptic equation to study the (2+1) -dimensional BBM equation. In the fifth section, we study the Higher order Coupled Burgers equation, get many new exact solutions, and provide theoretical foundation for the application of the equations. In the sixth section, we study the parametrical control of the exaqt solutions of the combined KdV equation. Because of the evolution equation with variable coefficients can reflect the variety of physical phenomena, it is very significant to study the effect of the temporal variation of the distributed parameters of the solitary wave solutions of the dynamical system.