| KdV-mKdV方程及其级数解 |
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| 引用本文： | 韦敏志,唐生强.KdV-mKdV方程及其级数解[J].桂林电子工业学院学报,2012(5):398-401. |
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| 作者姓名： | 韦敏志 唐生强 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院,广西桂林541004 |
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| 基金项目： | 国家自然科学基金（11061010,11161013） |
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| 摘 要： | 为研究KdV-mKdV方程的级数解,运用扩展的齐次平衡法,将KdV-mKdV方程约化成线性的偏微分方程,得到Bcklund变换以及KdV-mKdV方程的自变换解。通过Bcklund变换和该偏微分方程的多种级数解,获得丰富的精确解,包括多孤立波解、三角函数解和有理级数解。
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| 关 键 词： | KdV-mKdV方程 齐次平衡法 Bcklund变换 级数解 |
The KdV-mKdV equation and series solutions |
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| Wei Minzhi,Tang Shengqiang.The KdV-mKdV equation and series solutions[J].Journal of Guilin Institute of Electronic Technology,2012(5):398-401. |
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| Authors: | Wei Minzhi Tang Shengqiang |
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| Affiliation: | (School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China) |
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| Abstract: | The series solutions of the KdV-mKdV equation will be studied by using the extended homogenous balance method,we reduce the KdV-mKdV equation to a linear PDE and obtain Bcklund transformation of it.Furthermore,the self-transformation of solutions for the KdV-mKdV equation is obtained.By the Bcklund transformation and various series solutions of the PDE,abundant exact solutions of the KdV-mKdV equation are obtained including the multi-solitary wave solution,trigonometric function series solution,rational series solution and solution consisting of the three types of solutions. |
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| Keywords: | KdV-mKdV equation homogenous balance method Bcklund transformation series solution |
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