The European Physical Journal D

, Volume 58, Issue 1, pp 141–146

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

Nonlinear Dynamics

DOI: 10.1140/epjd/e2010-00075-x

Cite this article as:
Chen, Q., Kevrekidis, P. & Malomed, B. Eur. Phys. J. D (2010) 58: 141. doi:10.1140/epjd/e2010-00075-x


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.

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Department of Physical ElectronicsSchool of Electrical Engineering, Faculty of Engineering, Tel Aviv UniversityTel AvivIsrael

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