Dynamics of counterpropagating waves in parametrically forced systems

Martel, Carlos and Knobloch, Edgar and Vega de Prada, José Manuel (2000). Dynamics of counterpropagating waves in parametrically forced systems. "Physica D: Nonlinear Phenomena", v. 137 (n. 1-2); pp. 94-123. ISSN 0167-2789. https://doi.org/10.1016/S0167-2789(99)00170-0.

Description

Title: Dynamics of counterpropagating waves in parametrically forced systems
Author/s:
  • Martel, Carlos
  • Knobloch, Edgar
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Physica D: Nonlinear Phenomena
Date: February 2000
ISSN: 0167-2789
Volume: 137
Subjects:
Freetext Keywords: Parametrically excited waves; Amplitude equations; Counterpropagating waves; Multiple scale techniques
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

Parametrically driven waves in weakly dissipative systems with one extended dimension are considered. Multiple scale techniques are used to derive amplitude equations describing the interaction between counterpropagating waves. Dissipation, detuning and forcing are all assumed to be weak and any coupling to mean fields (such as large scale flows in fluid systems) is ignored. If the aspect ratio is moderately large the system is described by a pair of nonlocal equations for the (complex) amplitudes of the waves. The dynamics of these equations are studied both in annular and bounded geometries with lateral walls. The equations admit spatially uniform solutions in the form of standing waves and spatially nonuniform solutions with both simple and complex time-dependence. Transitions among these states are investigated as a function of the driving in three particular cases.

More information

Item ID: 6009
DC Identifier: http://oa.upm.es/6009/
OAI Identifier: oai:oa.upm.es:6009
DOI: 10.1016/S0167-2789(99)00170-0
Official URL: http://www.sciencedirect.com
Deposited by: Memoria de Investigacion 2
Deposited on: 15 Feb 2011 11:15
Last Modified: 20 Apr 2016 14:40
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