摘要

利用方法并借助數(shù)學(xué)軟件,獲得了對稱正則長波方程的許多行波

解, 包括孤立波解及三角函數(shù)周期解.并用軟件獲得幾種典型的波形圖.本文用

的方法還可以用到其他的非線性發(fā)展方程中去.

關(guān)鍵詞: 對稱正則長波方程; -展開法; -函數(shù)法; 方法;  行波解;

   齊次平衡原則

ABSTRACT

In this paper, with the aids of the symbolic mathematical software-Maple, we obtained traveling wave solutions of symmetric regularized long wave equation. These traveling wave solutions include solitary wave solutions and trigonometric functions periodic solution. Some typical waveforms of these traveling wave solutions are obtained by Maple software. Obviously, the method which has been used in this paper is also can be used to other nonlinear evolution equations.

Keywords:  Symmetric regularized long wave equation;  F- expansion method; 

The exp-function method; F-Exp method;  Traveling wave solution;

Homogeneous balance principle

目 錄

第一章 引言 1

1.1 方程介紹 1

1.2 方法簡述 2

第二章 對稱正則長波方程的精確解 3

2.1 對稱正則長波方程的一般解 3

2.2利用Exp-方法求方程Riccati方程的精確解 4

2.3 對稱正則長波方程的精確解 12

2.4 幾種典型的波形圖 16

第三章 結(jié)論 18

參考文獻(xiàn) 19

致謝 21