Backlund transformation of partial differential equations from the Painleve-Gambier classification. I. Kaup-Kupershmidt equation

被引：36

作者：

Musette, M ^{[1
]}

Conte, R

机构：

[1] Free Univ Brussels, Dienst Theoret Nat Kunde, B-1050 Brussels, Belgium

[2] CEA Saclay, Serv Phys Etat Condense, F-91191 Gif Sur Yvette, France

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1998年 / 39卷 / 10期

关键词：

D O I：

10.1063/1.532554

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Among the 50 nonlinear second-order differential equations of Painleve' and Gambier, those which are linearizable provide a natural scheme for deriving the Lax pair and the Darboux transformation of a nonlinear partial differential equation when the order of the scattering problem is three. This new method allows one to obtain, from singularity analysis only, the Backlund transformation of the Kaup-Kupershmidt equation, a result which was missing until now. (C) 1998 American Institute of Physics. [S0022-2488(98)03610-X].

引用

页码：5617 / 5630

页数：14

共 41 条

[1] SYSTEMS OF ORDINARY DIFFERENTIAL-EQUATIONS WITH NON-LINEAR SUPERPOSITION PRINCIPLES [J].

ANDERSON, RL ;

HARNAD, J ;

WINTERNITZ, P .

PHYSICA D, 1982, 4 (02) :164-182

[2]

BACKLUND AV, 1883, LUNDS U ARSSKRIFT AV, V2, P19

[3] THE INVERSE PROBLEM FOR THE 3RD ORDER EQUATION UXXX+Q(X)UX+R(X)U=-IZETA-3U [J].

CAUDREY, PJ .

PHYSICS LETTERS A, 1980, 79 (04) :264-268

[4] About third order and higher order differential equations whose general integrals are at critical fixed points [J].

Chazy, J .

ACTA MATHEMATICA, 1911, 34 (04) :317-385

[5] GENERAL DERIVATION OF BACKLUND TRANSFORMATIONS FROM INVERSE SCATTERING PROBLEMS [J].

CHEN, HH .

PHYSICAL REVIEW LETTERS, 1974, 33 (15) :925-928

[6]

CONT R, 1990, INVERSE METHODS ACTI, P497

[7] LINEARITY INSIDE NONLINEARITY - EXACT-SOLUTIONS TO THE COMPLEX GINZBURG-LANDAU EQUATION [J].

CONTE, R ;

MUSETTE, M .

PHYSICA D, 1993, 69 (1-2) :1-17

[8]

CONTE R, 1991, NONLINEAR AND CHAOTIC PHENOMENA IN PLASMA, SOLIDS AND FLUIDS, P94

[9] INVARIANT PAINLEVE ANALYSIS OF PARTIAL-DIFFERENTIAL EQUATIONS [J].

CONTE, R .

PHYSICS LETTERS A, 1989, 140 (7-8) :383-390

[10] THE 2-SINGULAR MANIFOLD METHOD .2. CLASSICAL BOUSSINESQ SYSTEM [J].

CONTE, R ;

MUSETTE, M ;

PICKERING, A .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (01) :179-187

← 1 2 3 4 5 →