On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case

Annales de l’institut Fourier ◽

10.5802/aif.1730 ◽

1999 ◽

Vol 49 (5) ◽

pp. 1581-1602 ◽

Author(s):

Yannick Gâtel ◽

Dimitri Yafaev

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Radiation Conditions ◽

Conditions At Infinity

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On solutions of the Schrödinger equation with radiation conditions at infinity

ADVSOV - Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations ◽

10.1090/advsov/007/07 ◽

1991 ◽

pp. 179-204 ◽

Author(s):

D. Yafaev

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Radiation Conditions ◽

Conditions At Infinity

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Propagation of Analytic Singularities for Short and Long Range Perturbations of the Free Schrödinger Equation

Algebraic and Analytic Microlocal Analysis - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-030-01588-6_12 ◽

2018 ◽

pp. 575-587

Author(s):

André Martinez ◽

Shu Nakamura ◽

Vania Sordoni

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Analytic Singularities

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Beyond Nonlinear Schrodinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interactions

Journal of Nonlinear Mathematical Physics ◽

10.2991/jnmp.2001.8.supplement.24 ◽

2001 ◽

Vol 8 (Supplement) ◽

pp. 139

Author(s):

D GRECU ◽

Anca VISINESCU ◽

A S CARSTEA

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Long Range Interactions

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Long-Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.21701 ◽

2017 ◽

Vol 70 (12) ◽

pp. 2300-2365 ◽

Author(s):

Gino Biondini ◽

Dionyssios Mantzavinos

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Modulational Instability ◽

Nonlinear Schrodinger Equation ◽

Time Asymptotics ◽

Long Time ◽

Nonzero Boundary ◽

Long Time Asymptotics ◽

Conditions At Infinity

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Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013113 ◽

2014 ◽

Vol 48 (2) ◽

pp. 411-431 ◽

Author(s):

Christophe Gomez ◽

Olivier Pinaud

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Splitting Scheme ◽

Long Range Correlations ◽

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Long range scattering for the nonlinear Schrödinger equation with higher order anisotropic dispersion in two dimensions

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.123638 ◽

2020 ◽

Vol 483 (2) ◽

pp. 123638 ◽

Author(s):

Jean-Claude Saut ◽

Jun-ichi Segata

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Two Dimensions ◽

Nonlinear Schrödinger ◽

Anisotropic Dispersion

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Asymptotics for the Schrödinger equation with a repulsive delta potential and a long-range dissipative nonlinearity

Asymptotic Analysis for Nonlinear Dispersive and Wave Equations ◽

10.2969/aspm/08110013 ◽

2019 ◽

Author(s):

Masahiro Ikeda

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Delta Potential ◽

Dissipative Nonlinearity

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Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2006.10.041 ◽

2007 ◽

Vol 378 (2) ◽

pp. 223-237 ◽

Author(s):

Nickolay Korabel ◽

George M. Zaslavsky

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Range Interaction ◽

Nonlinear Schrödinger ◽

Transition To Chaos ◽

Long Range Interaction

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Integral boundary conditions for the time-dependent Schrödinger equation: Superposition of the laser field and a long-range atomic potential

Physical Review A ◽

10.1103/physreva.62.015401 ◽

2000 ◽

Vol 62 (1) ◽

Author(s):

A. M. Ermolaev ◽

A. V. Selin

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Laser Field ◽

Schrodinger Equation ◽

Integral Boundary Conditions ◽

Time Dependent ◽

Integral Boundary ◽

Atomic Potential

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Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interactions

Journal of Nonlinear Mathematical Physics ◽

10.2991/jnmp.2001.8.s.24 ◽

2001 ◽

Vol 8 (sup1) ◽

pp. 139-144 ◽

Author(s):

D Grecu ◽

Anca Vis¸inescu ◽

A S Cârstea

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Long Range Interactions

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