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

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.