Eur. Phys. J. D 58, 141-146 (2010)
https://doi.org/10.1140/epjd/e2010-00075-x

Formation of fundamental solitons in the two-dimensional nonlinear Schrödinger equation with a lattice potential

¹ Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003-4515, USA
² Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

Corresponding author: malomed@eng.tau.ac.il

Received: 11 August 2009
Revised: 17 January 2010
Published online: 23 March 2010

Abstract

We consider self-trapping of 2D solitons in the model based on the Gross-Pitaevskii/nonlinear Schrödinger equation with the self-attractive cubic nonlinearity and a periodic potential of the optical-lattice (OL) type. It is known that this model may suppress the collapse, giving rise to a family of stable fundamental solitons. Here, we report essential dynamical features of self-trapping of the fundamental solitons from input configurations of two types, with vorticity 0 or 1. We identify regions in the respective parameter spaces corresponding to the formation of the soliton, collapse, and decay. A noteworthy result is the self-trapping of stable fundamental solitons in cases when the input norm essentially exceeds the collapse threshold. We also compare predictions of the dynamical variational approximation with direct numerical simulations.