Long time motion of NLS solitary waves in a confining potential

Abstract

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.

arXiv comment42 pages, 2 figures

References in corpus (5)

• Solitary Wave Dynamics in an External Potential
• Selection of the ground state for nonlinear Schroedinger equations
• Asymptotic stability of N-soliton states of NLS
• Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation
• Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

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