Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.
Bibliographical note© 2016 American Physical Society. Pattern Generation by Dissipative Parametric Instability. A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas. Phys. Rev. Lett. 116, 028701 – Published 13 January 2016
-Funding: Spanish Ministerio de Educación y Ciencia; European FEDER Project
(FIS2011-29731-C02-01); ERC project ULTRALASER, the Russian Ministry of Education and Science (14.B25.31.0003); Russian Foundation for Basic Research (15-02-07925); Presidential Grant for Young Researchers (188.8.131.52-MK); the Dinasty Foundation; Russian Science Foundation (Grant No. 14-21-00110); and ICONE Project through the Marie Curie Grant (608099)