ORBITAL STABILITY OF STANDING WAVES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH POTENTIAL

DOI10.1142/S0129055X01001095zbMath1038.35112OpenAlexW2032010770MaRDI QIDQ4418319

Patricio L. Felmer, Carlos Cid

Publication date: 7 August 2003

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

Full work available at URL: https://doi.org/10.1142/s0129055x01001095

zbMATH Keywords

nonlinear Schrödinger equationstability of standing waves

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (5)

Standing waves for nonlinear Schrödinger equations with a general nonlinearity ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations ⋮ Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term ⋮ Nonlinear Schrödinger equation with a point defect ⋮ Stable directions for small nonlinear Dirac standing waves

Cites Work

• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Stability theory of solitary waves in the presence of symmetry. I
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• On a class of nonlinear Schrödinger equations
• Existence of solitary waves in higher dimensions
• Semi-classical states for nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Multi-peak bound states for nonlinear Schrödinger equations
• On concentration of positive bound states of nonlinear Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Uniqueness of ground states for quasilinear elliptic equations
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting

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