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物理学报. 2001, 50(4): 577-585.
doi: 10.7498/aps.50.577.
具有物理背景的高维Painlevé可积模型
- 收稿日期: 2000-02-02
- 修回日期: 2000-08-04
- 刊出日期: 2001-02-05
摘要: 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Painlevé可积模型.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Painlevé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,某些近似解可以成为精确解
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关键词:
- 高维可积模型 /
- “M?bious”不变 /
- 近似方法
English Abstract
HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELSWITH REAL PHYSICAL SIGNIFICATION
- Received Date:
02 February 2000
- Accepted Date:
04 August 2000
- Published Online:
05 February 2001
Abstract: 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.
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