## 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

#### 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
Revised: 14 July 2008
Accepted: 22 October 2008
First available in Project Euclid: 20 December 2017

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

#### 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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