Pattern generation by dissipative parametric instability
Abstract
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic antiphase modulation of spectrally-dependent losses arranged in a zig-zag way: an effective filtering is imposed at symmetrically located wavenumbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of the both key classical concepts of modulation instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate how 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.
Cite
@article{arxiv.1512.03482,
title = {Pattern generation by dissipative parametric instability},
author = {A. M. Perego and N. Tarasov and D. V. Churkin and S. K. Turitsyn and K. Staliunas},
journal= {arXiv preprint arXiv:1512.03482},
year = {2016}
}