SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRODINGER HIERARCHY AND ITS SIMILARITY REDUCTION

被引：27

作者：

Kakei, Saburo ^{[1
]}

Kikuchi, Tetsuya ^{[2
]}

机构：

[1] Rikkyo Univ, Dept Math, Toshima Ku, Tokyo 1718501, Japan

[2] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

来源：

GLASGOW MATHEMATICAL JOURNAL | 2005年 / 47A卷

关键词：

D O I：

10.1017/S0017089505002326

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The hierarchy structure of a derivative nonlinear Schrodinger equation is investigated in terms of the Sato-Segal-Wilson formulation. Special solutions are constructed as ratios of Wronski determinants. Relations to the Painleve IV and the discrete Painleve I are discussed by applying a similarity reduction.

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收藏

页码：99 / 107

页数：9

相关论文

共 14 条

[1] A CONNECTION BETWEEN NON-LINEAR EVOLUTION-EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF P-TYPE .2. [J].

ABLOWITZ, MJ ;

RAMANI, A ;

SEGUR, H .

JOURNAL OF MATHEMATICAL PHYSICS, 1980, 21 (05) :1006-1015

[2]

DATE E, 1982, OSAKA J MATH, V19, P125

[3]

Drinfeld V.G., 1984, J SOVIET MATH, V30, P1975

[4] SOLITON-SOLUTIONS OF NON-LINEAR EVOLUTION-EQUATIONS [J].

FREEMAN, NC .

IMA JOURNAL OF APPLIED MATHEMATICS, 1984, 32 (1-3) :125-145

[5] SOLITON-SOLUTIONS OF THE KORTEWEG-DEVRIES AND KADOMTSEV-PETVIASHVILI EQUATIONS - THE WRONSKIAN TECHNIQUE [J].

FREEMAN, NC ;

NIMMO, JJC .

PHYSICS LETTERS A, 1983, 95 (01) :1-3

[6]

Gerdjikov V. S., 1983, Bulgarian Journal of Physics, V10, P130

[7] From continuous Painleve IV to the asymmetric discrete Painleve I [J].

Grammaticos, B ;

Ramani, A .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (27) :5787-5798

[8] BILINEARIZATION OF A GENERALIZED DERIVATIVE NONLINEAR SCHRODINGER-EQUATION [J].

KAKEI, S ;

SASA, N ;

SATSUMA, J .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1995, 64 (05) :1519-1523

[9]

Kakei S, 2004, INT MATH RES NOTICES, V2004, P4181

[10] Hierarchy of (2+1)-dimensional nonlinear Schrodinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras [J].

Kakei, S ;

Ikeda, T ;

Takasaki, K .

ANNALES HENRI POINCARE, 2002, 3 (05) :817-845