| 通过Painlevé分析从低维模型中寻找高维可积模型 |
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| 引用本文： | 王晓波,贾曼,楼森岳.通过Painlevé分析从低维模型中寻找高维可积模型[J].宁波大学学报(理工版),2020,33(5):114-120. |
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| 作者姓名： | 王晓波 贾曼 楼森岳 |
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| 作者单位： | 宁波大学 物理科学与技术学院, 浙江 宁波 315211 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金;宁波市自然科学基金;宁波大学王宽诚幸福基金 |
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| 摘 要： | 将Painlevé方法推广到更一般的形式, 可以从给定的低维可积模型中得到无穷多个新的可积模型. 新的可积模型与原模型相比都是较高维的, 它们保持保角不变性和Painlevé性质. 本文主要以KdV、NLS和KP方程为例, 运用WTC法、截断展开、领头项分析等方法, 给出了(3+1)维可积模型的具体形式.
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| 关 键 词： | Painlevé分析 高维可积模型 低维可积模型 |
In search of higher dimensional integrable models from lower ones via Painlevé analysis |
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| WANG Xiaobo,JIA Man,LOU Senyue.In search of higher dimensional integrable models from lower ones via Painlevé analysis[J].Journal of Ningbo University(Natural Science and Engineering Edition),2020,33(5):114-120. |
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| Authors: | WANG Xiaobo JIA Man LOU Senyue |
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| Affiliation: | School of Physical Science and Technology, Ningbo University, Ningbo 315211, China |
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| Abstract: | Extending the Painlevé approach to a more general form, one can obtain infinitely many new integrable models in the context that they possess conformal invariance and the Painlevé property in any space dimensions from a given lower dimensional integrable model. This paper mainly focuses on taking the Korteweg-de Vries, nonlinear Schr?dinger and Kadomtsev-Petviashvili equations as simple examples, some explicit (3+1)-dimensional integrable models are given using the methods proposed by Weiss, Tabor, and Carnevale, as well as through truncation expansion and the leading order analysis. |
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| Keywords: | Painlevé analysis higher dimensional integrable models lower dimensional integrable models |
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