Long-time asymptotic behavior of a mixed Schrödinger equation with weighted Sobolev initial data

Qiaoyuan Cheng; Yiling Yang; Engui Fan

doi:10.1063/5.0045970

Long-time asymptotic behavior of a mixed Schrödinger equation with weighted Sobolev initial data

Journal of Mathematical Physics ◽

10.1063/5.0045970 ◽

2021 ◽

Vol 62 (9) ◽

pp. 093507

Author(s):

Qiaoyuan Cheng ◽

Yiling Yang ◽

Engui Fan

Keyword(s):

Asymptotic Behavior ◽

Initial Data ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Long Time ◽

Time Asymptotic Behavior

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Long-time asymptotic behavior for a fourth-order dispersive nonlinear Schrödinger equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125560 ◽

2021 ◽

pp. 125560

Author(s):

Yu-Feng Wang ◽

Nan Liu ◽

Bo-Ling Guo

Keyword(s):

Asymptotic Behavior ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Long Time ◽

Time Asymptotic Behavior

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Long-time asymptotic behavior of the modified Schrödinger equation via ∂¯-steepest descent method

Nonlinear Systems and Their Remarkable Mathematical Structures ◽

10.1201/9781003087670-15 ◽

2021 ◽

pp. 389-439

Author(s):

Yiling Yang ◽

Engui Fan

Keyword(s):

Asymptotic Behavior ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Descent Method ◽

Steepest Descent ◽

Steepest Descent Method ◽

Long Time ◽

Time Asymptotic Behavior

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Long time asymptotic behavior of the focusing nonlinear Schrödinger equation

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2017.08.006 ◽

2018 ◽

Vol 35 (4) ◽

pp. 887-920 ◽

Cited By ~ 8

Author(s):

Michael Borghese ◽

Robert Jenkins ◽

Kenneth D.T.-R. McLaughlin

Keyword(s):

Asymptotic Behavior ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Long Time ◽

Time Asymptotic Behavior

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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

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On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data

SIAM Journal on Mathematical Analysis ◽

10.1137/19m1279964 ◽

2020 ◽

Vol 52 (6) ◽

pp. 5892-5993

Author(s):

Tamara Grava ◽

Alexander Minakov

Keyword(s):

Asymptotic Behavior ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

Long Time ◽

Time Asymptotic Behavior

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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

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Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition

Proceedings of the American Mathematical Society ◽

10.1090/proc/13917 ◽

2017 ◽

Vol 146 (4) ◽

pp. 1713-1729 ◽

Cited By ~ 64

Author(s):

Shou-Fu Tian ◽

Tian-Tian Zhang

Keyword(s):

Boundary Condition ◽

Asymptotic Behavior ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation ◽

Time Periodic ◽

Time Asymptotic Behavior

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Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data

Journal of Differential Equations ◽

10.1016/j.jde.2020.08.003 ◽

2021 ◽

Vol 270 ◽

pp. 694-724 ◽

Cited By ~ 1

Author(s):

Yan Rybalko ◽

Dmitry Shepelsky

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Time Asymptotics ◽

Long Time ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Long Time Asymptotics ◽

Nonlocal Nonlinear

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Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2017.04.002 ◽

2018 ◽

Vol 35 (1) ◽

pp. 217-265 ◽

Cited By ~ 17

Author(s):

Jiaqi Liu ◽

Peter A. Perry ◽

Catherine Sulem

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Time Behavior ◽

Long Time Behavior ◽

Nonlinear Schrödinger ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation

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Defocusing Nonlocal Nonlinear Schrödinger Equation with Step-like Boundary Conditions: Long-time Behavior for Shifted Initial Data

Zurnal matematiceskoj fiziki analiza geometrii ◽

10.15407/mag16.04.418 ◽

2020 ◽

Vol 16 (4) ◽

pp. 418-453

Author(s):

Yan Rybalko ◽

◽

Dmitry Shepelsky ◽

Keyword(s):

Initial Data ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Time Behavior ◽

Long Time Behavior ◽

Long Time ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Nonlocal Nonlinear

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