Dynamics near the origin of the long range scattering for the one-dimensional Schrödinger equation

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

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A new proof of long-range scattering for critical nonlinear Schrödinger equations.
Long range scattering for the wave-Schrödinger system revisited
Analyticity of the scattering operator for semilinear dispersive equations
Domain and range of the modified wave operator for Schrödinger equations with a critical nonlinearity
Long range scattering for the Maxwell-Schrödinger system with arbitrarily large asymptotic data
Long range scattering for nonlinear Schrödinger equations in one space dimension
Geometric optics and long range scattering for one-dimensional nonlinear Schrödinger equations
Modified scattering for the critical nonlinear Schrödinger equation
Modified wave operators without loss of regularity for some long range Hartree equations. II
Modified wave operators without loss of regularity for some long-range Hartree equations. I
Long range scattering and modified wave operators for the Maxwell-Schrödinger system. II: The general case
A remark on long-range scattering for the Hartree type equation
MODIFIED WAVE OPERATORS FOR NONLINEAR SCHRÖDINGER EQUATIONS IN LOWER ORDER SOBOLEV SPACES
Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
WAVE OPERATORS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A NONLINEARITY OF LOW DEGREE IN ONE OR TWO SPACE DIMENSIONS
Long Range Scattering for Nonlinear Schrödinger Equations with Critical Homogeneous Nonlinearity
Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions
Modified Scattering Operator for the Derivative Nonlinear Schrödinger Equation
Scattering and small data completeness for the critical nonlinear Schrödinger equation
The scattering map determines the nonlinearity
Long range scattering and modified wave operators for some Hartree type equations. III: Gevrey spaces and low dimensions
Recovery of the nonlinearity from the modified scattering map

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