Determinant representation of Darboux transformation for the AKNS system

被引：94

作者：

He Jingsong ^{[1
]}

Zhang Ling ^{[1
]}

Cheng Yi ^{[1
]}

Li Yishen ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Anhua 230026, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2006年 / 49卷 / 12期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

darboux transformation; AKNS system (Ablowitz-Kaup-Newell-Segur System); determinant; soliton surface;

D O I：

10.1007/s11425-006-2025-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The n-fold Darbouxtransform (DT) is a 2x2 matrix for the Ablowitz-Kaup-Newell-Segur (AKNS) system. In this paper, each element of this matrix is expressed by 2n + 1 ranks' determinants. Using these formulae, the determinant expressions of eigenfunctions generated by the n-fold DT are obtained. Furthermore, we give out the explicit forms of the n-soliton surface of the Nonlinear Schrodinger Equation (NLS) by the determinant of eigenfunctions.

引用

页码：1867 / 1878

页数：12

共 24 条

[1]

Ablowitz M.J., 1991, SOLITONS NONLINEAR E

[2] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE [J].

ABLOWITZ, MJ ;

KAUP, DJ ;

NEWELL, AC ;

SEGUR, H .

PHYSICAL REVIEW LETTERS, 1973, 31 (02) :125-127

[3]

BOBENKO AI, 1994, HARMONIC MAPS INTEGR, P83

[4] SOLVING THE KP HIERARCHY BY GAUGE TRANSFORMATIONS [J].

CHAU, LL ;

SHAW, JC ;

YEN, HC .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 149 (02) :263-278

[5] EXACT SOLUTION TO LOCALIZED-INDUCTION-APPROXIMATION EQUATION MODELING SMOKE RING MOTION [J].

CIESLINSKI, J ;

GRAGERT, PKH ;

SYM, A .

PHYSICAL REVIEW LETTERS, 1986, 57 (13) :1507-1510

[6]

CIESLINSKI J, 1991, J MATH PHYS, V32, P2395, DOI 10.1063/1.529165

[7] DETERMINANTS OF MATRICES OVER NONCOMMUTATIVE RINGS [J].

GELFAND, IM ;

RETAKH, VS .

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1991, 25 (02) :91-102

[8]

GU CH, 1987, LETT MATH PHYS, V13, P179, DOI 10.1007/BF00423444

[9]

Gu CH., 1999, DARBOUX TRANSFORMATI

[10] The determinant representation of the gauge transformation operators [J].

He, JS ;

Li, YS ;

Cheng, Y .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2002, 23 (04) :475-486

← 1 2 3 →