具有物理背景的高维Painlev可积模型

HIGHER DIMENSIONAL PAINLEV? INTEGRABLE MODELS WITH REAL PHYSICAL SIGNIFICATION

提出了一种求解任意维数非线性模型的“M bious”变换下不变的渐进展开方法 ,并可同时获得许多新的与原模型有着相同维数的Painlev啨可积腜?.取 (2 +1)维KdV Burgers(KdVB)方程和Kadomtsev Petviashvili(KP)方程为具体例子 ,获得了一些新的具有Painlev啨性质的高维“Ｍ bious”变换下不变的方程及原模型的近似解 .在某些特殊情况下 。

A “Mbius” invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimension is proposed. Many new Painlevé integrable models with the same dimension can be obtained at the same time. Taking the (2+1)\|dimensional KdV\|Burgers(KdVB) equation, (3+1)\|dimensional Kudomtsev\|Petviashvili (KP) equation as concrete examples, we obtain some new higher dimensional “Mbius” invariant models with Painlevé property and the approximate solutions of these models. In some special case, some approximate solutions become exact.