title: Localized modes in dissipative lattice media: an overview.
abstract: We give an overview of recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, one-dimensional solitons feature motion regimes in the form of the transverse drift and persistent swing. In the two-dimensional geometry, three types of axisymmetric radial lattices are considered, namely those based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick.
authors.affiliation: School of Electronics and Information, Guangdong Polytechnic Normal University, 510665 Guangzhou, People's Republic of China.
authors.forename: Yingji
authors.initials: Y
authors.lastname: He
authors.affiliation: Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel malomed@post.tau.ac.il.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.affiliation: Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania Horia Hulubei National Institute for Physics and Nuclear Engineering, POB MG-6, 077125 Magurele-Bucharest, Romania.
authors.forename: Dumitru
authors.initials: D
authors.lastname: Mihalache
keywords: complex Ginzburg–Landau equation; dissipative lattices; localized nonlinear modes; parity-time symmetry