Analysis & PDE

  • Anal. PDE
  • Volume 1, Number 3 (2008), 267-322.

Dynamics of nonlinear Schrödinger/Gross–Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes

Gang Zhou and Michael Weinstein

Full-text: Open access

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.

Article information

Source
Anal. PDE, Volume 1, Number 3 (2008), 267-322.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513797975

Digital Object Identifier
doi:10.2140/apde.2008.1.267

Mathematical Reviews number (MathSciNet)
MR2490293

Zentralblatt MATH identifier
1175.35136

Subjects
Primary: 35Q51: Soliton-like equations [See also 37K40] 37K40: Soliton theory, asymptotic behavior of solutions 37K45: Stability problems

Keywords
soliton nonlinear bound state nonlinear scattering asymptotic stability dispersive partial differential equation

Citation

Zhou, Gang; Weinstein, Michael. Dynamics of nonlinear Schrödinger/Gross–Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes. Anal. PDE 1 (2008), no. 3, 267--322. doi:10.2140/apde.2008.1.267. https://projecteuclid.org/euclid.apde/1513797975


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