通过Painlevé分析从低维模型中寻找高维可积模型  

In search of higher dimensional integrable models from lower ones via Painlevéanalysis

作　　者：王晓波 贾曼[1] 楼森岳[1] WANG Xiaobo;JIA Man;LOU Senyue(School of Physical Science and Technology,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学物理科学与技术学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2020年第5期114-120,共7页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：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。

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.Extending the Painlevéapproach to a more general form,one can obtain infinitely many new integrable models in the context that they possess conformal invariance and the Painlevéproperty in any space dimensions from a given lower dimensional integrable model.This paper mainly focuses on taking the Korteweg-de Vries,nonlinear Schrödinger 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.

关 键 词：PAINLEVÉ分析 高维可积模型 低维可积模型 

分 类 号：O415[理学—理论物理]