Long Range Scattering for Nonlinear Schrödinger Equations with Critical Homogeneous Nonlinearity

DOI10.1137/17M1144829zbMath1397.35284arXiv1612.04524OpenAlexW2748839376MaRDI QIDQ4568374

Satoshi Masaki, Hayato Miyazaki

Publication date: 21 June 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.04524

zbMATH Keywords

asymptotic behaviorscatteringnonlinear Schrödinger equationsmodified wave operatorlong range scattering

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (7)

Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions ⋮ Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions ⋮ Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials ⋮ Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions ⋮ Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential ⋮ Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators ⋮ Lifespan of Solutions to Nonlinear Schrödinger Equations with General Homogeneous Nonlinearity of the Critical Order

Cites Work

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• The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension
• Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces.
• On the critical nongauge invariant nonlinear Schrödinger equation
• Nonexistence of scattering states for some quadratic nonlinear Schrödinger equations in two space dimensions.
• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Long-range scattering for nonlinear Schrödinger equations in one and two space dimensions.
• Nonexistence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in two space dimensions.
• Nonlinear ground state representations and sharp Hardy inequalities
• Existence of solutions for Schrödinger evolution equations
• Long range scattering for nonlinear Schrödinger equations in one space dimension
• Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\)
• Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
• Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms
• MODIFIED WAVE OPERATORS FOR NONLINEAR SCHRÖDINGER EQUATIONS IN LOWER ORDER SOBOLEV SPACES
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• The asymptotic behavior of nonlinear Schrödinger equations
• Logarithmic Time Decay for the Cubic Nonlinear Schrödinger Equations
• 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
• On the asymptotics for cubic nonlinear Schrödinger equations
• Large Time Behavior for the Cubic Nonlinear Schrödinger Equation
• The dissipative property of a cubic non-linear Schrödinger equation

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