Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator

DOI10.1134/S1061920807020057zbMath1125.35092arXivmath/0608780OpenAlexW2098876744MaRDI QIDQ996561

Alexander I. Komech, Andrew Komech

Publication date: 21 September 2007

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

Full work available at URL: https://arxiv.org/abs/math/0608780

zbMATH Keywords

global well-posednesslocal well-posednessasymptotic stability of solitary wavesweak global attractors

Mathematics Subject Classification ID

Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) PDEs in connection with quantum mechanics (35Q40)

Related Items (6)

The point-like limit for a NLS equation with concentrated nonlinearity in dimension three ⋮ Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity ⋮ On Asymptotic Stability of Solitary Waves in Schrödinger Equation Coupled to Nonlinear Oscillator ⋮ The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit ⋮ Existence of solitary waves for the discrete Schrödinger equation coupled to a nonlinear oscillator ⋮ The One-Dimensional Dirac Equation With Concentrated Nonlinearity

Cites Work

• On the global attraction to solitary waves for the Klein-Gordon equation coupled to a nonlinear oscillator

This page was built for publication: Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator