Standing waves in a complex Ginzburg-Landau equation with time-delay feedback

Michael Stich; Carsten Beta

doi:10.3934/proc.2011.2011.1329

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2011, Volume 2011: 1329-1334. Doi: 10.3934/proc.2011.2011.1329 open access

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Standing waves in a complex Ginzburg-Landau equation with time-delay feedback

Michael Stich^1, and
Carsten Beta^2,

1.
Centro de Astrobiología (CSIC-INTA), Ctra. de Ajalvir, km. 4, 28850 Torrejón de Ardoz (Madrid)
2.
Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, Haus 28, 14476 Potsdam

Received: August 2010

Revised: April 2011

Published: August 2017

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Abstract

Standing waves are studied as solutions of a complex Ginzburg- Landau equation subjected to local and global time-delay feedback terms. The onset of standing waves is studied at the instability of the homogeneous periodic solution with respect to spatially periodic perturbations. The solution of this spatiotemporal wave pattern is given and is compared to the homogeneous periodic solution.

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Mathematics Subject Classification: Primary: 35K57; 35B10; Secondary: 35Q92.

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