Long time behavior of solutions of nonlinear classical field equations: The example of NLS defocusing
type: Item
instance of: scholarly article
title: Long time behavior of solutions of nonlinear classical field equations: The example of NLS defocusing
zbMATH Open document ID: 0785.35099
DOI: 10.1016/0167-2789(92)90166-K
author: Yves Pomeau
published in: Physica D
publication date: 1994-01-31T00:00:00Z
review text: Nonlinear and nonintegrable classical fields cannot relax for long times toward an ill defined thermal equilibrium. The specific example considered here is the long time dynamics of solutions of the nonlinear Schrödinger equation, in the defocusing case. I show, under some assumptions, that for long times a cascade of energy toward smaller and smaller scales introduces a kind of dissipation in a system that is formally reversible, and I give the scaling laws for this. Besides this relaxation by weak interaction between phonons, there is also a relaxation of localized vortical structures emitting phonons.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 81V15
zbMATH DE Number: 493564
zbMATH Keywords: dissipation
zbMATH Keywords: scaling laws
zbMATH Keywords: localized vortical structures
MaRDI profile type: Publication
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full work available at URL: 0167-2789(92)90166-k
OpenAlex ID: W2053599276
description: scientific article; zbMATH DE number 493564