# On the Amplitude Equations Arising at the Onset of the Oscillatory Instability in Pattern Formation

Vega de Prada, José Manuel (1992). On the Amplitude Equations Arising at the Onset of the Oscillatory Instability in Pattern Formation. "SIAM Journal on Mathematical Analysis", v. 24 (n. 3); pp. 603-617. ISSN 0036-1410.

## Description

Title: On the Amplitude Equations Arising at the Onset of the Oscillatory Instability in Pattern Formation Vega de Prada, José Manuel Article SIAM Journal on Mathematical Analysis September 1992 24 pattern formation, oscillatory instability, amplitude equations, Ginzburg-Landau equations E.T.S.I. Aeronáuticos (UPM) Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014] Recognition - No derivative works - Non commercial

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## Abstract

A well-known system of two amplitude equations is considered that describes the weakly nonlinear evolution of many nonequilibrium systems at the onset of the so-called oscillatory instability. Those equations depend on a small parameter, $\varepsilon$, that is a ratio between two distinguished spatial scales. In the limit $\varepsilon \to 0$, a simpler asymptotic model is obtained that consists of two complex cubic Ginzburg–Landau equations, coupled only by spatially averaged terms.

Item ID: 6212 http://oa.upm.es/6212/ oai:oa.upm.es:6212 Memoria de Investigacion 2 01 Mar 2011 10:10 20 Apr 2016 15:31

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