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Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrödinger lattices

Uta Naether1,2, Rodrigo A. Vicencio1,2, and Magnus Johansson3,*

  • 1Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
  • 2Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile
  • 3Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden

  • *mjn@ifm.liu.se; http://people.ifm.liu.se/majoh
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Phys. Rev. E 83, 036601 – Published 7 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036601

Abstract

We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to the existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.

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Phys. Rev. E 83, 036601– Published 7 March, 2011
  • Received 8 October 2010

©2011 American Physical Society

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