title: Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity.
abstract: We consider a two-dimensional (2D) generalization of a recently proposed model [Gligorić et al., Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being those considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (also analytically, when possible). Typical scenarios of instability development are exhibited through direct simulations.
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA and Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.affiliation: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Avadh
authors.initials: A
authors.lastname: Saxena
authors.affiliation: Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: A R
authors.initials: AR
authors.lastname: Bishop
authors.affiliation: Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece.
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis