Dissipative nonlinear Schrödinger equations for large data in one space dimension

DOI10.3934/cpaa.2020044zbMath1436.35291OpenAlexW2981308747MaRDI QIDQ2286204

Gaku Hoshino

Publication date: 10 January 2020

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2020044

zbMATH Keywords

asymptotic behaviornonlinear Schrödinger equationstime decay estimatedissipative nonlinearity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (6)

Asymptotic behavior for solutions to the vector nonlinear Schrödinger equations ⋮ Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension ⋮ Scattering for solutions of a dissipative nonlinear Schrödinger equation ⋮ Asymptotic behavior for solutions to the dissipative nonlinear Schrödinger equations with the fractional Sobolev space ⋮ Global well-posedness and analytic smoothing effect for the dissipative nonlinear Schrödinger equations ⋮ Upper and lower \(L^2\)-decay bounds for a class of derivative nonlinear Schrödinger equations

Cites Work

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• A new proof of long-range scattering for critical nonlinear Schrödinger equations.
• Remarks on proofs of conservation laws for nonlinear Schrödinger equations
• Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data
• 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 \(n\geq{}2\)
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity.
• Time decay for nonlinear dissipative Schrödinger equations in optical fields
• On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equation in 2D.
• Critical nonlinear Schrödinger equations with data in homogeneous weighted \(\mathbf L^2\) spaces
• The initial value problem for nonlinear Schrödinger equations with a dissipative nonlinearity in one space dimension
• Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity
• On Schrödinger systems with cubic dissipative nonlinearities of derivative type
• Fourier Analysis and Nonlinear Partial Differential Equations
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Analyticity of Submarkovian Semigroups
• Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities
• Introduction to nonlinear dispersive equations

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