SEMICLASSICAL LIMIT OF A CLASS OF SCHRÖDINGER EQUATIONS WITH POTENTIAL

DOI10.1081/PDE-120002870zbMath0998.35052MaRDI QIDQ4547613

Sahbi Keraani

Publication date: 24 November 2002

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

zbMATH Keywords

WKB methodWigner measurenonlinear focusing Schrödinger equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (12)

Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves ⋮ Geodesics and the Einstein nonlinear wave system ⋮ The geodesic hypothesis and non-topological solitons on pseudo-Riemannian manifolds ⋮ The nonlinear Schrödinger equation: solitons dynamics ⋮ Nonlinear coherent states and Ehrenfest time for Schrödinger equation ⋮ LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL ⋮ Semiclassical limit for a NLS with harmonic potential. ⋮ Interaction of coherent states for Hartree equations ⋮ On the dynamics of solitons in the nonlinear Schrödinger equation ⋮ ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL ⋮ Long‐time dynamics of KdV solitary waves over a variable bottom ⋮ Soliton dynamics for the nonlinear Schrödinger equation with magnetic field

Cites Work

• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• On Wigner measures
• Ergodic properties of eigenfunctions for the Dirichlet problem
• Semiclassical states of nonlinear Schrödinger equations
• Soliton dynamics in a potential
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
• Oscillations of concentration effects in semilinear dispersive wave equations
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Homogenization limits and Wigner transforms

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