Translator Disclaimer
2008 Dynamics of nonlinear Schrödinger/Gross–Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes
Gang Zhou, Michael Weinstein
Anal. PDE 1(3): 267-322 (2008). DOI: 10.2140/apde.2008.1.267

Abstract

Nonlinear Schrödinger/Gross–Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (“excited states”) and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system’s large time asymptotic relaxation to the ground state (soliton) manifold.

Citation

Download Citation

Gang Zhou. Michael Weinstein. "Dynamics of nonlinear Schrödinger/Gross–Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes." Anal. PDE 1 (3) 267 - 322, 2008. https://doi.org/10.2140/apde.2008.1.267

Information

Received: 9 January 2008; Revised: 14 July 2008; Accepted: 22 October 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1175.35136
MathSciNet: MR2490293
Digital Object Identifier: 10.2140/apde.2008.1.267

Subjects:
Primary: 35Q51, 37K40, 37K45

Rights: Copyright © 2008 Mathematical Sciences Publishers

JOURNAL ARTICLE
56 PAGES


SHARE
Vol.1 • No. 3 • 2008
MSP
Back to Top