The initial value problem for nonlinear Schrödinger equations with a dissipative nonlinearity in one space dimension

DOI10.1007/S00028-016-0327-5zbMath1367.35157OpenAlexW2307033590MaRDI QIDQ2397780

Yuanfeng Jin, Guangzhi Jin, Chun-Hua Li

Publication date: 23 May 2017

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-016-0327-5

zbMATH Keywords

large time asymptoticslarge initial datasubcritical NLS equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (14)

Optimal \(L^2\)-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity ⋮ Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations ⋮ Asymptotic behavior for solutions to the vector nonlinear Schrödinger equations ⋮ Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime ⋮ Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations ⋮ The effect of gain and strong dissipative structures on nonlinear Schrödinger equations in optical fiber ⋮ Optimal \(L^2\)-decay of solutions to the dissipative nonlinear Schrödinger equation in higher space dimensions ⋮ Scattering for solutions of a dissipative nonlinear Schrödinger equation ⋮ On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D ⋮ Dissipative nonlinear Schrödinger equations for large data in one space dimension ⋮ Asymptotic behavior for solutions to the dissipative nonlinear Schrödinger equations with the fractional Sobolev space ⋮ On the derivative nonlinear Schrödinger equation with weakly dissipative structure ⋮ 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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• Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
• Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data
• 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
• Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities
• A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimension
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities

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