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Spatial solitons under competing linear and nonlinear diffractions

Y. Shen, P. G. Kevrekidis, and N. Whitaker

Boris A. Malomed

  • Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

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

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Phys. Rev. E 85, 026606 – Published 27 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.026606

Abstract

We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, which is found in an exact analytical form, along with the largest total power (norm) that the waves may possess. Past a critical point, collapse effects are observed, caused by suitable perturbations. Interactions between two identical parallel solitary beams are explored by dint of direct numerical simulations. It is found that in-phase solitons merge into robust or collapsing pulsons, depending on the strength of the nonlinear diffraction.

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Phys. Rev. E 85, 026606– Published 27 February, 2012
  • Received 26 December 2011

©2012 American Physical Society

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