Finite size effects near the onset of the oscillatory instability

Martel, Carlos and Vega de Prada, José Manuel (1996). Finite size effects near the onset of the oscillatory instability. "Nonlinearity", v. 9 (n. 5); pp. 1129-1171. ISSN 0951-7715. https://doi.org/10.1088/0951-7715/9/5/005.

Description

Title: Finite size effects near the onset of the oscillatory instability
Author/s:
  • Martel, Carlos
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Nonlinearity
Date: September 1996
ISSN: 0951-7715
Volume: 9
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects.

More information

Item ID: 5988
DC Identifier: http://oa.upm.es/5988/
OAI Identifier: oai:oa.upm.es:5988
DOI: 10.1088/0951-7715/9/5/005
Official URL: http://iopscience.iop.org/0951-7715/9/5/005
Deposited by: Memoria de Investigacion 2
Deposited on: 14 Feb 2011 10:11
Last Modified: 20 Apr 2016 14:39
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