(2+1)维色散长波方程组新的无穷序列精确解

J4 ›› 2010, Vol. 27 ›› Issue (4): 402-410.

(2+1)维色散长波方程组新的无穷序列精确解

套格图桑¹,斯仁道尔吉²

内蒙古师范大学数学科学学院，呼和浩特 010022

收稿日期:2009-08-20 修回日期:2009-10-19 出版日期:2010-07-28 发布日期:2010-06-13
通讯作者: 套格图桑，（1964-），硕士，副教授，研究方向为孤立子与可积系统理论及其应用。 E-mail:tgts@imnu.edu.cn
基金资助:
国家自然科学基金（10461006）,内蒙古自治区高等学校科学研究基金（NJZZ07031），内蒙古自治区自然科学基金（200408020103），内蒙古师范大学自然科学青年研究计划（QN005023）

New infinite sequence exact solutions of a set of (2+1)-dimensional dispersive wave equations

Taogetusang¹, Sirendaoerji²

College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Received:2009-08-20 Revised:2009-10-19 Published:2010-07-28 Online:2010-06-13

摘要/Abstract

摘要：

为了获得非线性发展方程的无穷序列新精确解, 给出Riccati方程的一些新解和B\"{a}cklund变换以及解的非线性叠加公式, 并Riccati方程与函数变换相结合,借助符号计算系统Mathematica,构造了 (2+1)维维色散长波方程组新的无穷序列精确解. 这些解包括无穷序列类孤子解、无穷序列复合型解等. 这种方法构造非线性发展方程无穷序列精确解领域具有普遍意义.

关键词: Riccati方程, B¨acklund变换, 非线性叠加公式, 精确解

Abstract:

To seek new infinite sequence exact solutions to nonlinear evolution equations, the formula of nonlinear superposition of some new solutions and B\"{a}cklund transformation of Riccati equation are given, and combing Riccati equation with function transformation, new infinite sequence exact solutions to a set of (2+1)-dimensional dispersive wave equations are constructed with the aid of symbolic computation system Mathematica, which include infinite sequence soliton-like solutions and infinite sequence complexiton solutions. The method is of significance to seek infinite sequence exact solutions to other nonlinear evolution equations.

Key words: Riccati equation, B¨acklund transformation, the formula of nonlinear superposition, exact solution

套格图桑斯仁道尔吉. (2+1)维色散长波方程组新的无穷序列精确解[J]. J4, 2010, 27(4): 402-410.

Taogetusang, Sirendaoerji. New infinite sequence exact solutions of a set of (2+1)-dimensional dispersive wave equations[J]. J4, 2010, 27(4): 402-410.

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