Long-time asymptotics of the nonlinear Schrödinger equation shock problem

Robert Buckingham; Stephanos Venakides

doi:10.1002/cpa.20179

Long-time asymptotics of the nonlinear Schrödinger equation shock problem

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.20179 ◽

2007 ◽

Vol 60 (9) ◽

pp. 1349-1414 ◽

Cited By ~ 44

Author(s):

Robert Buckingham ◽

Stephanos Venakides

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Long-Time Asymptotics for the Integrable Nonlocal Focusing Nonlinear Schrödinger Equation for a Family of Step-Like Initial Data

Communications in Mathematical Physics ◽

10.1007/s00220-021-03941-2 ◽

2021 ◽

Vol 382 (1) ◽

pp. 87-121

Author(s):

Yan Rybalko ◽

Dmitry Shepelsky

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.124188 ◽

2020 ◽

Vol 489 (2) ◽

pp. 124188

Author(s):

Qiaoyuan Cheng ◽

Engui Fan

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.5036705 ◽

2019 ◽

Vol 60 (3) ◽

pp. 031504 ◽

Cited By ~ 9

Author(s):

Yan Rybalko ◽

Dmitry Shepelsky

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Long Time Asymptotics ◽

Nonlocal Nonlinear

Download Full-text

Long-time asymptotics for the generalized coupled derivative nonlinear Schrödinger equation

Nonlinear Systems and Their Remarkable Mathematical Structures ◽

10.1201/9781003087670-11 ◽

2021 ◽

pp. 272-304

Author(s):

Mingming Chen ◽

Xianguo Geng ◽

Kedong Wang ◽

Bo Xue

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation ◽

Long Time Asymptotics

Download Full-text

Long time asymptotics for the focusing nonlinear Schrödinger equation in the solitonic region with the presence of high-order discrete spectrum

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125635 ◽

2021 ◽

pp. 125635

Author(s):

Zhaoyu Wang ◽

Meisen Chen ◽

Engui Fan

Keyword(s):

Schrödinger Equation ◽

Discrete Spectrum ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

High Order ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

The Gelfand-Levitan-Marchenko equation and the long-time asymptotics of the solutions of the nonlinear Schrödinger equation

L. D. Faddeev’s Seminar on Mathematical Physics - American Mathematical Society Translations: Series 2 ◽

10.1090/trans2/201/05 ◽

2000 ◽

pp. 63-78

Author(s):

A. M. Budylin ◽

V. S. Buslaev

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Marchenko Equation ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Long-time Asymptotics for the Integrable Discrete Nonlinear Schrödinger Equation: the Focusing Case

Funkcialaj Ekvacioj ◽

10.1619/fesi.62.227 ◽

2019 ◽

Vol 62 (2) ◽

pp. 227-253 ◽

Cited By ~ 1

Author(s):

Hideshi Yamane

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II

Symmetry Integrability and Geometry Methods and Applications ◽

10.3842/sigma.2015.020 ◽

2015 ◽

Cited By ~ 1

Author(s):

Hideshi Yamane

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Long Time Asymptotics

Download Full-text

Curved wedges in the long‐time asymptotics for the integrable nonlocal nonlinear Schrödinger equation

Studies in Applied Mathematics ◽

10.1111/sapm.12403 ◽

2021 ◽

Author(s):

Yan Rybalko ◽

Dmitry Shepelsky

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Long Time Asymptotics ◽

Nonlocal Nonlinear

Download Full-text

Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line

Nonlinearity ◽

10.1088/1361-6544/aa84c6 ◽

2017 ◽

Vol 30 (11) ◽

pp. 4141-4172 ◽

Cited By ~ 9

Author(s):

Lynnyngs Kelly Arruda ◽

Jonatan Lenells

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Half Line ◽

Nonlinear Schrödinger ◽

Time Asymptotics ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation ◽

Long Time Asymptotics

Download Full-text