| 一些非线性发展方程的周期解 |
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| 引用本文： | 杨丽英,刘官厅.一些非线性发展方程的周期解[J].内蒙古师范大学学报(自然科学版),2004,33(3):256-261. |
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| 作者姓名： | 杨丽英 刘官厅 |
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| 作者单位： | [1]内蒙古农业大学基础部，内蒙古呼和浩特010018 [2]内蒙古师范大学数学科学学院．内蒙古呼和浩特010022 |
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| 基金项目： | ProjectSupportedbytheNationalNaturalScienceFoundationofChina(10372016)andtheNaturalScienceFoundationofInnerMongolia( 2 0 0 3 0 80 2 0 10 1) |
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| 摘 要： | 利用辅助椭圆方程给出了求解非线性发展方程的精确周期解的一种代数方法，借助计算机的符号计算，求得了mKdV方程和非线性Klein-Gordon方程的多种精确周期解，这些解包括了已有的用Jacobi椭圆函数展开法所求得的周期解．在极限情形下，退化为相应的孤立波解或冲击波解．
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| 关 键 词： | 非线性发展方程 周期解 辅助椭圆方程 符号计算 mKdV方程 |
Periodic Solutions of Some Nonlinear Evolution Equations |
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| Abstract.Periodic Solutions of Some Nonlinear Evolution Equations[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2004,33(3):256-261. |
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| Authors: | Abstract |
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| Abstract: | By using the solutions of an auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.Many exact periodic solutions of mKdV equation and Klein-Gorden equation are explicitly obtained with the aid of symbolic computation.At limit condition,they give corresponding solitary wave or shock wave solutions. |
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| Keywords: | auxiliary equation method nonlinear evolution equation periodic solution symbolic computation |
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