The Research Of Solving The Solutions Of Some Kinds Of Nonlinear Evolution Equations With Arbitrary Order And The Property Of The Solutions

With the help of the symbolic computation system Mathematic, the paper researches two problems. First, with the help of the auxiliary equation method and the trial function method, the new soliton and so on solutions of some kinds of nonlinear evolution equations with constant coefficients (variety coefficients) are constructed. These solutions are consisting of Jacobi elliptic function, hyperbolic function, trigonometric function and rational function new solutions. Second, by the image of the solutions, the paper researches some property of the solutions.The first chapter put forward the history of the produce and the developing of the soliton theory, and introduces the present developing situation of some methods of solving the solutions of the nonlinear evolution equations.The second chapter put forward three kinds of auxiliary equations and their new solutions, and new solutions of generalized KdV equation, generalized KP-Burgers equation and so on some kinds of generalized nonlinear evolution equations are constructed, and by the image of the solutions, the chapter researches some property of the solutions. These solutions are consisting of hyperbolic cosecant function, hyperbolic tangent function, hyperbolic secant function, hyperbolic cotangent function and cosecant function. And with the help of the Backlund transformation of the solutions of the second kind of elliptic equation, the new infinite sequence solutions of the generalized BBM equation are constructed. These solutions are consisting of elliptic function.The third chapter with the trial function method and the symbolic computation system Mathematic, the new soliton-like solutions consisting of hyperbolic function and trigonometric function of the generalized variable coefficient fifth-older KdV equation are obtained, and by the image of the solutions, the chapter researches some property of the solutions.In the forth chapter, with the help of the Backlund transformation of the Riccati equation and the nonlinear superposition formula of solutions, by the symbolic computation system Mathematica, the new infinite sequence soliton-like solutions consisting of exponential function, trigonometric function and rational function of the general (2+1)-dimension Calogero -Bogoyav lenskii-Schiff system are constructed, then the chapter researches the property of the solutions.