title: 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 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.
authors.affiliation: Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom.|Departament de Fisica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, E-08222 Barcelona, Spain.
authors.forename: A M
authors.initials: AM
authors.lastname: Perego
authors.affiliation: Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom.|Institute of Computational Technologies SB RAS, Novosibirsk 630090, Russia.
authors.forename: N
authors.initials: N
authors.lastname: Tarasov
authors.affiliation: Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom.|Novosibirsk State University, Novosibirsk 630090, Russia.|Institute of Automation and Electrometry SB RAS, Novosibirsk 630090, Russia.
authors.forename: D V
authors.initials: DV
authors.lastname: Churkin
authors.affiliation: Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom.|Novosibirsk State University, Novosibirsk 630090, Russia.
authors.forename: S K
authors.initials: SK
authors.lastname: Turitsyn
authors.affiliation: Departament de Fisica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, E-08222 Barcelona, Spain.|Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, E-08010 Barcelona, Spain.
authors.forename: K
authors.initials: K
authors.lastname: Staliunas
mesh_terms: D008962:Models, Theoretical; D017711:Nonlinear Dynamics