| 一族非线性色散偏微分方程的指数函数型和三角函数型精确解 |
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| 引用本文： | 张金华,丁玉敏. 一族非线性色散偏微分方程的指数函数型和三角函数型精确解[J]. 西南大学学报(自然科学版), 2012, 0(1): 28-33 |
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| 作者姓名： | 张金华 丁玉敏 |
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| 作者单位： | 红河学院数学系 |
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| 基金项目： | 云南省自然科学基金资助项目(2008CD186) |
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| 摘 要： | 利用辅助方程法和指数函数法,研究了由Degasperis,Holm和Hone 3人导出的一族非线性三阶扩散方程.借助于Maple程序的辅助计算,获得了大量的指数函数型、双曲函数型和三角函数型精确解,这些精确解包括孤立波解、扭子波解和周期波解,并分析和讨论了几种典型类型的精确解的动力学性质,给出了几种代表性精确解的波形图.
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| 关 键 词： | 一族非线性三阶扩散方程 指数函数法 辅助方程法 周期波解 孤立波解 扭子波解 |
Exact Solutions of Exp-function-Type and Trigonometric Function-Type to a Family of Nonlinear Third-Order PDEs |
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| ZHANG Jin-hua,DING Yu-min. Exact Solutions of Exp-function-Type and Trigonometric Function-Type to a Family of Nonlinear Third-Order PDEs[J]. Journal of southwest university (Natural science edition), 2012, 0(1): 28-33 |
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| Authors: | ZHANG Jin-hua DING Yu-min |
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| Affiliation: | Department of Mathematics,Honghe University,Mengzi Yunnan 661100,China |
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| Abstract: | Using the auxiliary equation method and the exp-function method,we study a family of third-order nonlinear dispersive PDEs,given by Degasperis,Holm and Hone.By the auxiliary computation of Maple’s programe,many exact solutions of exp-function type,hyperbolic function type and trigonometric function type are obtained,including solitary wave solutions,kink-wave solutions and periodic wave solutions.The dynamic properties of several typical exact solutions are analyzed and discussed and several typical waveforms are illustrated. |
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| Keywords: | a family of third-order nonlinear dispersive PDEs exp-function method auxiliary equation method periodic wave solution solitary wave solution Kink-wave solution |
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