| sine-Gordon型方程的无穷序列新精确解 |
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| 引用本文： | 套格图桑.sine-Gordon型方程的无穷序列新精确解[J].物理学报,2011,60(7):70203-070203. |
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| 作者姓名： | 套格图桑 |
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| 作者单位： | 内蒙古师范大学数学科学学院,呼和浩特 010022 |
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| 基金项目： | 国家自然科学基金(批准号:10461006); 内蒙古自治区高等学校科学研究基金(批准号:NJZZ07031); 内蒙古自治区自然科学基金(批准号:2010MS0111)资助的课题~~ |
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| 摘 要： | 为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解.
关键词：
sine-Gordon型方程
解的非线性叠加公式
辅助方程
无穷序列精确解
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| 关 键 词： | sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解 |
| 收稿时间： | 2010-07-27 |
New infinite sequences exact solutions to sine-Gordon-type equations |
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| Taogetusang.New infinite sequences exact solutions to sine-Gordon-type equations[J].Acta Physica Sinica,2011,60(7):70203-070203. |
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| Authors: | Taogetusang |
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| Abstract: | In order to obtain infinite sequence exact solutions to the sine-Gordon-type equations, the auxiliary equations of triangular function type and hyperbolic function type, Bäcklund transformation and nonlinear superposition formula of the solutions are presented. And the method is used to construct new infinite sequence exact solutions to the sine-Gordon equation, mKdV-sine-Gordon equation, (n+1)- dimensional double sine-Gordon equation and the sinh-Gordon equation with the help of symbolic computation system Mathematica, which include infinite sequence triangular function solutions, the infinite sequence hyperbolic function solutions, infinite sequence Jacobi elliptic function solutions and infinite sequence computation solutions. |
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| Keywords: | sine-Gordon-type equations solution of nonlinear superposition formula auxiliary equation infinite sequence exact solution |
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