Explicit quasi-periodic solutions of the Kaup-Newell hierarchy

被引：19

作者：

Geng, Xianguo ^{[1
]}

Li, Zhu ^{[1
]}

Xue, Bo ^{[1
]}

Guan, Liang ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 425卷 / 02期

基金：

中国国家自然科学基金;

关键词：

The Kaup-Newell hierarchy; Quasi-periodic solutions; NONLINEAR SCHRODINGER-EQUATION; ALGEBRO-GEOMETRIC SOLUTIONS; BACKLUND-TRANSFORMATIONS; SOLITON-EQUATIONS; SPECTRAL PROBLEM; FORMULATION; SYSTEMS; FLOWS; MODEL;

D O I：

10.1016/j.jmaa.2015.01.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algebraic curve of arithmetic genus n is introduced with the aid of the Lax matrix, from which we construct the meromorphic function on the algebraic curve and investigate its properties. Further, we straighten out all the flows associated with the Kaup-Newell hierarchy under the Abel-Jacobi coordinates. Finally, we achieve the explicit quasi-periodic solutions for the whole Kaup-Newell hierarchy, including the coupled derivative nonlinear Schrodinger equations. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1097 / 1112

页数：16

共 31 条

[1] [Anonymous], 1976, PROGR THEORET PHYS S, V59, P107, DOI 10.1143/PTPS.59.107
[2] [Anonymous], 1984, Tata Lectures on Theta
[3] BACKLUND-TRANSFORMATIONS RELATED TO THE KAUP NEWELL SPECTRAL PROBLEM
BOITI, M
LADDOMADA, C
PEMPINELLI, F
TU, GZ
[J]. PHYSICA D, 1983, 9 (03): : 425 - 432
[4] A (2+1)-dimensional derivative Toda equation in the context of the Kaup-Newell spectral problem
Cao, Cewen
Yang, Xiao
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (02)
[5] PERTURBATION-THEORY FOR THE NEARLY INTEGRABLE NON-LINEAR EQUATIONS ASSOCIATED WITH A MODIFIED ZAKHAROV-SHABAT SCATTERING PROBLEM
DODD, RK
MORRIS, HC
EAGLETON, J
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (04): : 1455 - 1465
[6] A GENERALIZED KAUP-NEWELL SPECTRAL PROBLEM, SOLITON-EQUATIONS AND FINITE-DIMENSIONAL INTEGRABLE SYSTEMS
GENG, XG
MA, WX
[J]. NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA A-NUCLEI PARTICLES AND FIELDS, 1995, 108 (04): : 477 - 486
[7] Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations
Geng, XG
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (09): : 2289 - 2303
[8] Algebro-Geometric Solutions of the TD Hierarchy
Geng, Xianguo
Zeng, Xin
Xue, Bo
[J]. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2013, 16 (03) : 229 - 251
[9] DECOMPOSITION AND STRAIGHTENING OUT OF THE DISCRETE KAUP-NEWELL FLOWS
Geng, Xianguo
Su, Ting
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2011, 25 (32): : 4513 - 4531
[10] Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation
Geng, Xianguo
Ren, Hongfeng
He, Guoliang
[J]. PHYSICAL REVIEW E, 2009, 79 (05):

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