Nonlinear Dynamics

The European Physical Journal D

, Volume 58, Issue 1, pp 141-146

First online:

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

  • Q. Y. ChenAffiliated withDepartment of Mathematics and Statistics, University of Massachusetts
  • , P. G. KevrekidisAffiliated withDepartment of Mathematics and Statistics, University of Massachusetts
  • , B. A. MalomedAffiliated withDepartment of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University Email author 

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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.