Eur. Phys. J. D 50, 317-323 (2008)
https://doi.org/10.1140/epjd/e2008-00239-3

Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

¹ Laboratoire de Photonique Quantique et Moléculaire, CNRS, École Normale Supérieure de Cachan, UMR 8537, 94235 Cachan, France
² Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, 69978 Tel Aviv, Israel

Corresponding author: ^a radik@eng.tau.ac.il

Received: 2 April 2008
Published online: 12 December 2008

Abstract

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by cubic attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also stabilize various species of fundamental and vortical solitons against the supercritical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of all families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in “pancake” traps.