Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection

Martel, Carlos and Knobloch, Edgar and Vega de Prada, José Manuel (2003). Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection. "Physica D: Nonlinear Phenomena", v. 174 (n. 1-4); pp. 198-217. ISSN 0167-2789. https://doi.org/10.1016/S0167-2789(02)00691-7.

Description

Title: Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection
Author/s:
  • Martel, Carlos
  • Knobloch, Edgar
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Physica D: Nonlinear Phenomena
Date: January 2003
ISSN: 0167-2789
Volume: 174
Subjects:
Freetext Keywords: Parametric resonance; Counterpropagating waves; Weak dispersion; Faraday waves
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

The dynamics of parametrically driven counterpropagating waves in a one-dimensional extended nearly conservative annular system are described by two coupled, damped, parametrically driven nonlinear Schrödinger (NLS) equations with opposite transport terms due to the group velocity, and small dispersion. The system is characterized by two length scales defined by a balance between (a) forcing and dispersion (the dispersive scale), and (b) forcing and advection at the group velocity (the transport scale). Both are large compared to the basic wavelength of the pattern. The dispersive scale plays an important role in the structure of solutions arising from secondary instabilities of frequency-locked spatially uniform standing waves (SW), and manifests itself both in traveling pulses or fronts and in extended spatio-temporal chaos, depending on the signs of the dispersion coefficient and nonlinearity. Author Keywords: Parametric resonance; Counterpropagating waves; Weak dispersion; Faraday waves

More information

Item ID: 6053
DC Identifier: http://oa.upm.es/6053/
OAI Identifier: oai:oa.upm.es:6053
DOI: 10.1016/S0167-2789(02)00691-7
Official URL: http://www.sciencedirect.com
Deposited by: Memoria de Investigacion 2
Deposited on: 17 Feb 2011 10:18
Last Modified: 20 Apr 2016 14:41
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