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

  • Nonlinear Dynamics
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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003-4515, USA

    Q. Y. Chen & P. G. Kevrekidis

  2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    B. A. Malomed

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  1. Q. Y. Chen
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  2. P. G. Kevrekidis
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  3. B. A. Malomed
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Correspondence to B. A. Malomed.

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Chen, Q., Kevrekidis, P. & Malomed, B. Formation of fundamental solitons in the two-dimensional nonlinear Schrödinger equation with a lattice potential. Eur. Phys. J. D 58, 141–146 (2010). https://doi.org/10.1140/epjd/e2010-00075-x

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  • DOI: https://doi.org/10.1140/epjd/e2010-00075-x

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