HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

doi:10.1088/1009-1963/10/2/301

中国物理B ›› 2001, Vol. 10 ›› Issue (2): 87-96.doi: 10.1088/1009-1963/10/2/301

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HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

阮航宇¹, 陈一新²

(1)Institute of Modern Physics, Ningbo University, Ningbo 315211, China; Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China; (2)Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China

收稿日期:2000-06-04 出版日期:2001-02-15 发布日期:2005-06-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.19875041), and by the Natural Science Foundation of Zhejiang Province, China (Grant No.100033).

HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

Ruan Hang-yu (阮航宇)^ab, Chen Yi-xin (陈一新)^b

^a Institute of Modern Physics, Ningbo University, Ningbo 315211, China; ^b Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China

Received:2000-06-04 Online:2001-02-15 Published:2005-06-12
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.19875041), and by the Natural Science Foundation of Zhejiang Province, China (Grant No.100033).

摘要/Abstract

摘要： A conformal 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 Zabolotskaya-Khokhlov and Kudomtsev-Petviashvili (ZKKP) equation as concrete examples, we obtain some new higher dimensional conformal invariant models with Painlevé property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.

Abstract: A conformal 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 Zabolotskaya-Khokhlov and Kudomtsev-Petviashvili (ZKKP) equation as concrete examples, we obtain some new higher dimensional conformal invariant models with Painlevé property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.

Key words: higher dimension, conformal invariance, ZKKP equation

中图分类号: (Logic, set theory, and algebra)

02.10.-v

02.30.-f (Function theory, analysis)

阮航宇, 陈一新. HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS[J]. 中国物理B, 2001, 10(2): 87-96.

Ruan Hang-yu (阮航宇), Chen Yi-xin (陈一新). HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS[J]. Chinese Physics, 2001, 10(2): 87-96.

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HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

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