| 2+1维非线性发展方程的多种周期解 |
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| 引用本文： | 刘官厅,范天佑.2+1维非线性发展方程的多种周期解[J].内蒙古师范大学学报(自然科学版),2004,33(4):345-352. |
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| 作者姓名： | 刘官厅 范天佑 |
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| 作者单位： | [1]内蒙古师范大学数学科学学院，内蒙古呼和浩特010022 [2]北京理工大学理学院物理系，北京100081 |
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| 基金项目： | ProjectSupportedbytheNationalNaturalScienceFoundationofChina (10 3 72 0 16)，theInnerMongoliaNaturalScienceFoundation
(2 0 0 3 0 80 2 0 10 1)andtheKeyProgramofScientificResearchFoundationforYouthofInnerMongoliaNormalUniversity (QNZ0 0 111) |
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| 摘 要： | 利用一个辅助椭圆方程的解，将求解2 1维非线性发展方程精确解的问题转化为一个代数方程进行求解．借助计算机的符号计算．求得了KP方程和2 1维mKDV方程的多种精确周期解．在极限条件下，这些周期解退化为孤立波解．
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| 关 键 词： | 非线性发展方程 周期解 KP方程 孤立波解 椭圆方程 mKDV方程 精确解 计算机 符号计算 求解 |
Periodic Solutions of 2+1 Dimensional Nonlinear Evolution Equations |
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| Abstract.Periodic Solutions of 2+1 Dimensional Nonlinear Evolution Equations[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2004,33(4):345-352. |
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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 2+1 dimensional nonlinear evolution equations.It is shown that various exact periodic solutions of the KP equation and 2+1 dimensional mKdV equation are explicitly obtained in an unified way with the aid of symbolic computation.At limit condition,they give corresponding shock wave or solitary wave solutions. |
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| Keywords: | auxiliary equation method nonlinear evolution equation periodic solution symbolic computation solitary wave solution |
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