Darboux transformations of integrable couplings and applications

被引：73

作者：

Ma, Wen-Xiu ^{[1
,2
,3
,4
]}

Zhang, Yu-Juan ^{[5
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[4] North West Univ, Dept Math Sci, Int Inst Symmetry Anal & Math Modelling, Mafikeng Campus,Private Bag X2046, ZA-2735 Mmabatho, South Africa

[5] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

来源：

REVIEWS IN MATHEMATICAL PHYSICS | 2018年 / 30卷 / 02期

基金：

上海市自然科学基金; 美国国家科学基金会;

关键词：

Matrix spectral problem; integrable coupling; Darboux transformation; non-semisimple Lie algebra; soliton; SEMIDIRECT SUMS; LIE-ALGEBRAS; HAMILTONIAN STRUCTURES; SOLITON HIERARCHY; LOOP ALGEBRAS; EQUATIONS; EVOLUTION; SYSTEMS;

D O I：

10.1142/S0129055X18500034

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A formulation of Darboux transformations is proposed for integrable couplings, based on non-semisimple matrix Lie algebras. Applications to a kind of integrable couplings of the AKNS equations are made, along with an explicit formula for the associated Backlund transformation. Exact one-soliton-like solutions are computed for the integrable couplings of the second- and third-order AKNS equations, and a type of reduction is created to generate integrable couplings and their one-soliton-like solutions for the NLS and MKdV equations.

引用

页数：26

共 42 条

[1]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[2]

ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249

[3]

Chen D. Y., 2006, INTRO SOLITONS

[4]

Drinfeld V G., 1981, Sov. Math. Dokl, V23, P457

[5]

FOKAS AS, 1987, STUD APPL MATH, V77, P253

[6]

Frappat L., 2000, DICT LIE ALGEBRAS SU

[7]

Fuchssteiner B., 1979, NONLINEAR ANAL THEOR, V3, P849, DOI [10.1016/0362-546X(79)90052-X, DOI 10.1016/0362-546X(79)90052-X]

[8] NEW SOLITONS CONNECTED TO THE DIRAC-EQUATION [J].

GROSSE, H .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1986, 134 (5-6) :297-304

[9]

Gu C., 2004, Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry

[10] Nonlinear Schrodinger equation: Generalized Darboux transformation and rogue wave solutions [J].

Guo, Boling ;

Ling, Liming ;

Liu, Q. P. .

PHYSICAL REVIEW E, 2012, 85 (02)

← 1 2 3 4 5 →