通过Painlevé分析从低维模型中寻找高维可积模型
PDF下载 (311)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.DOI:
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 & Engineering Edition),2020,33(5):114-120.DOI:
| Title: | In search of higher dimensional integrable models from lower ones via Painlevé analysis |
| 作者: | 王晓波, 贾 曼, 楼森岳 |
| Author(s): | WANG Xiaobo, JIA Man, LOU Senyue |
| 关键词: | Painlevé分析; 高维可积模型; 低维可积模型; Painlevé analysis |
| Keywords: | higher dimensional integrable models; lower dimensional integrable models |
| 分类号: | O415 |
| 文献标识码: | A |
| 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. |
| 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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| 备注/Memo: | 收稿日期: 2020－05－11. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11975131, 11675084）; 宁波市自然科学基金（2015A610159）; 宁波大学王宽诚幸福基金. 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/第一作者: 王晓波（1993－）, 女, 山西忻州人, 在读硕士研究生, 主要研究方向: 非线性物理. E-mail: 1403421943@qq.com *通信作者: 楼森岳（1957－）, 男, 浙江宁波人, 教授, 主要研究方向: 非线性物理. E-mail: lousenyue@nbu.edu.cn |
