The Exact Solution Of The Nonlinear Evolution System Solution Automatically Research

Nonlinear evolution equation is a mathematical model for describing physical phenomenon which developing with time and is an important frontier field in the study of nonlinear physical, especially in the study of soliton theory. In recent years, nonlinear science has developed deeply and the solitary wave solutions of nonlinear evolution equation are widely studied in natural science and engineering technology, such as physics, biology, graphics, communication and so on.In my thesis, based on the study and research on the method of obtaining exact solitary wave solutions of nonlinear evolution equations and absorbed insight from the ideas of experts and scholars, we make a modification of the tanh-sech method and give an implementation of it in symbolic computation system Maple. We investigate several multidimensional nonlinear evolution equations with it. In order to make people to use this method better in studying nonlinear evolution equations, we present an automatized programme for solving and studying all kinds of multidimensional nonlinear evolution equations.In this thesis, we focus on the following four parts:In Section 1, we introduce the history about how to discover and how to propose the solitary wave, also we narrate the tortuous process of it from being oppugned by scientists to prove its existence in theoretical aspect and then how to get everyone's approve. Finally, we list several forms of solitary wave solutions that were found in the course of investigating solitary wave.In Section 2, we illustrate the idea and the principle of the method of constructing exact solutions for nonlinear evolution equations. Then a variety of typical methods of constructing exact solitary wave solutions are introduced, so that everyone has a profound understanding on this method.In Section 3, we introduce the principle of the improved tanh-sech method and show its necessity and effectiveness. Finally, we investigate several multidimensional nonlinear evolution equations by our symbolic computation Maple package, such as (2+1) KP equations, (2+1) Ito equations, (2+1) KD equations and (3+1) Burgers equations. The results demonstrate the improved tanh-sech method being effectiveness as a tool for solving solitary wave solutions of high-dimensional nonlinear evolution equations.In Section 4, we illustrate the operation principle and the loading method of the automated solving package ASTNS, also we analyses several high-dimensional nonlinear evolution equations by the ASTNS in Maple. It shows that the ASTNS is indeed effective and clear in the study of solitary wave solutions.Section 5 is a summary and short review of this work.