Long time motion of NLS solitary waves in a confining potential

DOI10.1007/s00023-006-0263-yzbMath1100.81019arXivmath-ph/0503009OpenAlexW2077925184MaRDI QIDQ2498076

B. Lars G. Jonsson, Jürg Fröhlich, Israel Michael Sigal, Stephen J. Gustafson

Publication date: 11 August 2006

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0503009

zbMATH Keywords

Lyapunov-Schmidt decompositionsolitary-wave solutionsgeneralized nonlinear Schrödinger equations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (28)

A generic framework of adiabatic approximation for nonlinear evolutions ⋮ Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves ⋮ Freezing of energy of a soliton in an external potential ⋮ Revisiting asymptotic stability of solitons of nonlinear Schrödinger equations via refined profile method ⋮ Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation ⋮ EFFECTIVE DYNAMICS FOR SOLITONS IN THE NONLINEAR KLEIN–GORDON–MAXWELL SYSTEM AND THE LORENTZ FORCE LAW ⋮ The nonlinear Schrödinger equation: solitons dynamics ⋮ Nonlinear coherent states and Ehrenfest time for Schrödinger equation ⋮ Nonlinear Dynamics of a System of Particle-Like Wavepackets ⋮ On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations ⋮ Solitons in the presence of a small, slowly varying perturbation ⋮ On weak interaction between a ground state and a non-trapping potential ⋮ Long time dynamics of highly concentrated solitary waves for the nonlinear Schrödinger equation ⋮ Solitary wave dynamics in time-dependent potentials ⋮ Newton's law for a trajectory of concentration of solutions to nonlinear Schrödinger equation ⋮ Invariant manifold of modified solitons for the perturbed sine-Gordon equation ⋮ Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time ⋮ Inelastic character of solitons of slowly varying gKdV equations ⋮ Interaction of coherent states for Hartree equations ⋮ On the dynamics of solitons in the nonlinear Schrödinger equation ⋮ Soliton-Potential Interactions for Nonlinear Schrödinger Equation in $\mathbb{R}^3$ ⋮ Long time oscillation of solutions of nonlinear Schrödinger equations near minimal mass ground state ⋮ A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II ⋮ Multiplicity and concentration results for local and fractional NLS equations with critical growth ⋮ Stability of the solitary manifold of the perturbed sine-Gordon equation ⋮ Soliton dynamics for the nonlinear Schrödinger equation with magnetic field ⋮ Colliding solitons for the nonlinear Schrödinger equation ⋮ Differential equations of quantum mechanics

This page was built for publication: Long time motion of NLS solitary waves in a confining potential