WAVE OPERATORS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A NONLINEARITY OF LOW DEGREE IN ONE OR TWO SPACE DIMENSIONS
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Publication:4474403
DOI10.1142/S021919970300121XzbMath1055.35112OpenAlexW2033285464MaRDI QIDQ4474403
Kazunori Moriyama, Satoshi Tonegawa, Yoshio Tsutsumi
Publication date: 12 July 2004
Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s021919970300121x
Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items (14)
MODIFIED WAVE OPERATORS FOR NONLINEAR SCHRÖDINGER EQUATIONS IN LOWER ORDER SOBOLEV SPACES ⋮ Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions ⋮ Long Range Scattering for Nonlinear Schrödinger Equations with Critical Homogeneous Nonlinearity ⋮ Final state problem for systems of cubic nonlinear Schrödinger equations in one dimension ⋮ Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions ⋮ Global solutions for 2D quadratic Schrödinger equations ⋮ Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials ⋮ Stability of the self-similar dynamics of a vortex filament ⋮ Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions ⋮ SCATTERING THEORY FOR ZAKHAROV EQUATIONS IN THREE-DIMENSIONAL SPACE WITH LARGE DATA ⋮ Final state problem for a quadratic nonlinear Schrödinger system in two space dimensions with mass resonance ⋮ Wave operators to a quadratic nonlinear Klein-Gordon equation in two space dimensions ⋮ Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities ⋮ Final state problem for a system of nonlinear Schrödinger equations with three wave interaction
Cites Work
- Global existence of small solutions to nonlinear evolution equations
- Long range scattering for nonlinear Schrödinger equations in one space dimension
- Rapidly decaying solutions of the nonlinear Schrödinger equation
- Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\)
- Decay and scattering of solutions of a nonlinear Schrödinger equation
- Modified wave operators for the derivative nonlinear Schrödinger equation
- Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
- The asymptotic behavior of nonlinear Schrödinger equations
- Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
- Global, small amplitude solutions to nonlinear evolution equations
- Global existence for a class of cubic nonlinear Schrödinger equations in one space dimension
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