Formation of fundamental solitons in the two-dimensional nonlinear Schrödinger equation with a lattice potential
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- Chen, Q., Kevrekidis, P. & Malomed, B. Eur. Phys. J. D (2010) 58: 141. doi:10.1140/epjd/e2010-00075-x
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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.