THE FOCUSING NONLINEAR SCHRÖDINGER EQUATION ON THE QUARTER PLANE WITH TIME-PERIODIC BOUNDARY CONDITION: A RIEMANN–HILBERT APPROACH

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748007000151 ◽

2007 ◽

Vol 6 (04) ◽

pp. 579 ◽

Author(s):

Anne Boutet de Monvel ◽

Vladimir Kotlyarov

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Quarter Plane ◽

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Blow-up of solutions for the nonlinear Schrödinger equation with quartic potential and periodic boundary condition

Lecture Notes in Mathematics - Functional-Analytic Methods for Partial Differential Equations ◽

10.1007/bfb0084910 ◽

1990 ◽

pp. 236-251 ◽

Author(s):

Takayoshi Ogawa ◽

Yoshio Tsutsumi

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Blow Up ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Quartic Potential

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Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in H12

Journal of Differential Equations ◽

10.1016/j.jde.2017.05.026 ◽

2017 ◽

Vol 263 (8) ◽

pp. 4658-4722 ◽

Author(s):

Razvan Mosincat

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation

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Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain) ◽

10.3934/proc.2015.0878 ◽

2015 ◽

Author(s):

Shoji Yotsutani ◽

Kunimochi Sakamoto ◽

Minoru Murai

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Traveling Waves ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Representation Formula ◽

Nonlinear Schrodinger Equation ◽

Derivative Nonlinear Schrödinger Equation

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On the Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition

International Mathematics Research Notices ◽

10.1155/imrn/2006/96763 ◽

2006 ◽

Author(s):

S. Herr

Keyword(s):

Boundary Condition ◽

Cauchy Problem ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

The Cauchy Problem ◽

Derivative Nonlinear Schrödinger Equation

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Construction of solutions of the defocusing nonlinear Schrödinger equation with asymptotically time‐periodic boundary values

Studies in Applied Mathematics ◽

10.1111/sapm.12285 ◽

2019 ◽

Vol 143 (4) ◽

pp. 404-448

Author(s):

Samuel Fromm

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Boundary Values ◽

Nonlinear Schrödinger ◽

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On the nonlinear Schrödinger equation with a boundary condition involving a time derivative of the field

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/abeb51 ◽

2021 ◽

Author(s):

Baoqiang Xia

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Time Derivative ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Time-periodic solitons in a damped-driven nonlinear Schrödinger equation

Physical Review E ◽

10.1103/physreve.83.056609 ◽

2011 ◽

Vol 83 (5) ◽

Author(s):

I. V. Barashenkov ◽

E. V. Zemlyanaya ◽

T. C. van Heerden

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a One-Sided Non-Zero Boundary Condition

Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations - Contemporary Mathematics ◽

10.1090/conm/651/13035 ◽

2015 ◽

pp. 157-194 ◽

Author(s):

B. Prinari ◽

F. Vitale

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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The nonlinear Schrödinger equation on the half-line with a Robin boundary condition

Analysis and Mathematical Physics ◽

10.1007/s13324-021-00589-y ◽

2021 ◽

Vol 11 (4) ◽

Author(s):

A. Alexandrou Himonas ◽

Dionyssios Mantzavinos

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Robin Boundary Condition ◽

Nonlinear Schrodinger Equation ◽

Half Line ◽

Nonlinear Schrödinger ◽

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On the spectral problem associated with the time-periodic nonlinear Schrödinger equation

Mathematische Annalen ◽

10.1007/s00208-019-01856-x ◽

2019 ◽

Vol 377 (3-4) ◽

pp. 1193-1264

Author(s):

Jonatan Lenells ◽

Ronald Quirchmayr

Keyword(s):

Schrödinger Equation ◽

Spectral Problem ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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