On dispersion managed nonlinear Schrödinger equations with lumped amplification

DOI10.1063/5.0053132zbMath1475.35312arXiv2009.10381OpenAlexW3186914720MaRDI QIDQ5009717

Young-Ran Lee, Mi-Ran Choi, Younghoon Kang

Publication date: 5 August 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.10381

zbMATH Keywords

Gabitov-Turitsyn or averaged equation

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum optics (81V80) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (4)

Averaging of nonlinear Schrödinger equations with time-oscillatory coefficients ⋮ Averaging of dispersion managed nonlinear Schrödinger equations ⋮ Well-posedness of dispersion managed nonlinear Schrödinger equations ⋮ Uniqueness of a Minimizer for a Variational Problem Related to the Dispersion Managed Nonlinear Schrödinger Equation

Cites Work

• Unnamed Item
• Unnamed Item
• On non-local variational problems with lack of compactness related to non-linear optics
• Remarks on proofs of conservation laws for nonlinear Schrödinger equations
• The nonlinear Schrödinger equation with white noise dispersion
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Well-posedness and averaging of NLS with time-periodic dispersion management
• A Schrödinger equation with time-oscillating nonlinearity
• Stability of dispersion managed solitons for vanishing average dispersion
• Exponential decay of dispersion managed solitons for vanishing average dispersion
• Exponential decay of dispersion-managed solitons for general dispersion profiles
• Well-posedness of dispersion managed nonlinear Schrödinger equations
• Endpoint Strichartz estimates
• On the well-posedness of the Cauchy problem for some nonlocal nonlinear Schrödinger equations
• Derivation of the Hartree equation for compound Bose gases in the mean field limit
• Thresholds for Existence of Dispersion Management Solitons for General Nonlinearities
• Stabilizing effects of dispersion management

This page was built for publication: On dispersion managed nonlinear Schrödinger equations with lumped amplification