A WAVE-EQUATION IN 2+1 - PAINLEVE ANALYSIS AND SOLUTIONS

被引：89

作者：

ESTEVEZ, PG ^{[1
]}

LEBLE, S ^{[1
]}

机构：

[1] KALININGRAD STATE UNIV,DEPT THEORET PHYS,KALININGRAD 236041,RUSSIA

来源：

INVERSE PROBLEMS | 1995年 / 11卷 / 04期

关键词：

D O I：

10.1088/0266-5611/11/4/018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the nonlinear equation m(ty) = (m(yxx) + m(x)m(y))(x) is throughly analysed. The Painleve test is performed yielding a positive result. The Backlund transformations are found and the Darboux-Moutard-Mahveev formalism arises in the context of this analysis. The singular manifold method, based upon the Painleve analysis, is proved to be a useful tool for generating solutions. Some interesting explicit expressions for one and two solitons are obtained and analysed in such a way.

引用

页码：925 / 937

页数：13

共 26 条

[1]

ABLOWITZ MJ, 1991, LECT NOTE SERIES, V149, P269

[2] ON THE CHARACTERIZATION OF MOUTARD TRANSFORMATIONS [J].

ATHORNE, C .

INVERSE PROBLEMS, 1993, 9 (02) :217-232

[3]

BOGOYAVLENSKII OI, 1990, USP MAT NAUK, V45, P17

[4] ON THE SPECTRAL TRANSFORM OF A KORTEWEG-DEVRIES EQUATION IN 2 SPATIAL DIMENSIONS [J].

BOITI, M ;

LEON, JJP ;

MANNA, M ;

PEMPINELLI, F .

INVERSE PROBLEMS, 1986, 2 (03) :271-279

[5] PAINLEVE EXPANSIONS FOR NONINTEGRABLE EVOLUTION-EQUATIONS [J].

CARIELLO, F ;

TABOR, M .

PHYSICA D, 1989, 39 (01) :77-94

[6] THE PAINLEVE PROPERTY, A MODIFIED BOUSSINESQ EQUATION AND A MODIFIED KADOMTSEV-PETVIASHVILI EQUATION [J].

CLARKSON, PA .

PHYSICA D, 1986, 19 (03) :447-450

[7] ON A SHALLOW-WATER WAVE-EQUATION [J].

CLARKSON, PA ;

MANSFIELD, EL .

NONLINEARITY, 1994, 7 (03) :975-1000

[8]

CLARKSON PA, 1994, P IMACS WORLD C COMP, P336

[9]

CLARKSON PA, 1994, M9436 U EX PREPR

[10] MODIFIED SINGULAR MANIFOLD EXPANSION - APPLICATION TO THE BOUSSINESQ AND MIKHAILOV-SHABAT SYSTEMS [J].

ESTEVEZ, PG ;

GORDOA, PR ;

ALONSO, LM ;

REUS, EM .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (08) :1915-1925

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