Remarks on Non-Linear Schrödinger Equation with Magnetic Fields

DOI10.1080/03605300801891927zbMath1159.35068arXivmath/0702882OpenAlexW2028295061MaRDI QIDQ3532796

Laurent Michel

Publication date: 28 October 2008

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702882

zbMATH Keywords

Sobolev spaceselectromagnetic fieldSchrödinger equationCauchy problems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (12)

SCHRÖDINGER SYSTEMS ARISING IN NONLINEAR OPTICS AND QUANTUM MECHANICS: PART I ⋮ Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials ⋮ Averaging of the nonlinear Schrödinger equation with highly oscillatory magnetic potentials ⋮ Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation ⋮ Threshold for blowup and stability for nonlinear Schrödinger equation with rotation ⋮ A note on stochastic Schrödinger equations with fractional multiplicative noise ⋮ Strong magnetic field limit in a nonlinear Iwatsuka-type model ⋮ On the Cauchy problem for the XFEL Schrödinger equation ⋮ Optimal Bilinear Control for the X-Ray Free Electron Laser Schrödinger Equation ⋮ A Conservative Discontinuous Galerkin Method for Nonlinear Electromagnetic Schrödinger Equations ⋮ A refined stability result for standing waves of the Schrödinger–Maxwell system ⋮ Soliton dynamics for the nonlinear Schrödinger equation with magnetic field

Cites Work

• Nonlinear Schrödinger equations with magnetic fields
• Geometric optics and instability for semi-classical Schrödinger equations
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• The classical field limit of scattering theory for non-relativistic many- boson systems. II
• Schrödinger evolution equations with magnetic fields
• Global existence and asymptotic behavior of solutions for the Maxwell- Schrödinger equations in three space dimensions
• Schrödinger operators with magnetic fields. I: General interactions
• Local well-posedness for the Maxwell-Schrödinger equation
• Semiclassical limit of the nonlinear Schrödinger equation in small time
• Maximal functions associated to filtrations

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