✦ LIBER ✦

A (3+1)-dimensional Painlevé integrable model obtained by deformation

✍ Scribed by Jun Yu; Zhimei Lou

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 70 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.281

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✦ Synopsis

Abstract

To find some non‐trivial higher‐dimensional integrable models (especially in (3+1) dimensions) is one of the most important problems in non‐linear physics. An efficient deformation method to obtain higher‐dimensional integrable models is proposed. Starting from (2+1)‐dimensional linear wave equation, a (3+1)‐dimensional non‐trivial non‐linear equation is obtained by using a non‐invertible deformation relation. Further, the Painlevé integrability of the resulting model is also proved. Copyright © 2002 John Wiley & Sons, Ltd.

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## Abstract A conformal invariant asymptotic expansion approach is used to solve the (3+1)‐dimensional non‐linear Schrödinger (NLS) equation. Some new (3+1)‐dimensional integrable models under the condition that they are conformal invariant and possess Painlevé property are obtained. These Painlevé