On the Cauchy problem for the nonlinear Schrödinger equations with time-dependent linear loss/gain
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Publication:488776
DOI10.1016/j.jmaa.2014.03.019zbMath1311.35281OpenAlexW2006703284MaRDI QIDQ488776
Dun Zhao, Chunyou Sun, Binhua Feng
Publication date: 26 January 2015
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.03.019
Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Phase transitions (general) in equilibrium statistical mechanics (82B26) Composite media; random media in optics and electromagnetic theory (78A48) Lasers, masers, optical bistability, nonlinear optics (78A60) Blow-up in context of PDEs (35B44)
Related Items (15)
Dynamics of blow-up solutions for the Schrödinger-Choquard equation ⋮ Sharp threshold of global existence and instability of standing wave for the Schrödinger-Hartree equation with a harmonic potential ⋮ The asymptotic property for nonlinear fourth-order Schrödinger equation with gain or loss ⋮ Stability of the Hartree equation with time-dependent coefficients ⋮ Existence and nonexistence of global solutions for time-dependent damped NLS equations ⋮ Stability of standing waves for the fractional Schrödinger-Hartree equation ⋮ Global existence and scattering for nonlinear Schrödinger equations with time-dependent damping ⋮ A random Schrödinger equation with time-oscillating nonlinearity and linear dissipation/gain ⋮ Global and non-global solutions for a class of damped fourth-order Schrödinger equations ⋮ Stability of standing waves for the fractional Schrödinger-Choquard equation ⋮ Optical solitons in nematic liquid crystals: model with saturation effects ⋮ On the blow-up solutions for the nonlinear Schrödinger equation with combined power-type nonlinearities ⋮ On the Cauchy problem for the XFEL Schrödinger equation ⋮ On damped non-linear Choquard equations ⋮ Optical solitons in nematic liquid crystals: arbitrary deviation angle model
Cites Work
- Unnamed Item
- Unnamed Item
- Blowup and scattering problems for the nonlinear Schrödinger equations
- Blow-up for the damped \(L^2\)-critical nonlinear Schrödinger equation
- Nonlinear Schrödinger equations and sharp interpolation estimates
- On the lowest eigenvalue of the Laplacian for the intersection of two domains
- Monotonicity properties of the blow-up time for nonlinear Schrödinger equations: numerical evidence
- Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: exponential and polynomial stabilization
- Remarks on global existence and blowup for damped nonlinear Schrödinger equations
- Blow-up solutions to the nonlinear Schrödinger equation with oscillating nonlinearities
- ``Mass concentration phenomenon for the nonlinear Schrödinger equation with the critical power nonlinearity. II
- Limiting profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
- Asymptotic smoothing effect for a weakly damped nonlinear Schrödinger equation in \(\mathbb{T}^2\)
- Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
- Long-time behaviour for weakly damped driven nonlinear Schrödinger equations in \(\mathbb{R}^ N, N\leq 3\)
- Well-posedness and averaging of NLS with time-periodic dispersion management
- A Schrödinger equation with time-oscillating nonlinearity
- Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in \(\mathbb{R}^2\)
- The limit behavior of solutions for the nonlinear Schrödinger equation including nonlinear loss/gain with variable coefficient
- Parametric resonance of ground states in the nonlinear Schrödinger equation
- Self-Focusing in the Damped Nonlinear Schrödinger Equation
- Soliton Management in Periodic Systems
- Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations
- Endpoint Strichartz estimates
- [https://portal.mardi4nfdi.de/wiki/Publication:4257011 Asymptotic and limiting profiles of blowup solutions of the nonlinear Schr�dinger equation with critical power]
- Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
- Matter wave switching in Bose–Einstein condensates via intensity redistribution soliton interactions
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