Inverse Scattering Transform for Nonlinear Schrodinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions

被引：5

作者：

Prinari, Barbara ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2023年 / 30卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Nonlinear Schrodinger systems; Integrable systems; Inverse scattering transform; Solitons; LONG-TIME ASYMPTOTICS; DISPERSIVE DIELECTRIC FIBERS; DEFOCUSING MANAKOV SYSTEM; ZAKHAROV-SHABAT OPERATOR; RIEMANN-HILBERT PROBLEMS; STEEPEST DESCENT METHOD; DARK SOLITONS; MODULATION INSTABILITY; DISCRETE EIGENVALUES; BOUNDARY-CONDITIONS;

D O I：

10.1007/s44198-023-00120-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line ( -8 < x < 8) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.

引用

页码：317 / 383

页数：67

共 196 条

[91]

Gerdjikov V.S., 1981, COMMUN JINR

[92] QUADRATIC BUNDLE AND NON-LINEAR EQUATIONS [J].