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Phys. Rev. E 77, 036614 (2008) [11 pages]

Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity

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F. Palmero* and R. Carretero-González
Nonlinear Dynamical Systems Group, Computational Science Research Center and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA

J. Cuevas
Grupo de Física No Lineal, Departamento de Física Aplicada I, EU Politécnica, Universidad de Sevilla, c/Virgen de África s/n, 41011-Sevilla, Spain

P. G. Kevrekidis
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

W. Królikowski
Centre for Ultra-high Bandwidth Devices (CUDOS), Nonlinear Physics Centre and Laser Physics Centre, Research School of Physical Science and Engineering, Australian National University, Canberra, ACT 0200, Australia

Received 13 December 2007; published 28 March 2008

In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are (a) the destabilization of the on-site mode centered at the defect in the repulsive case, (b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type, (c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects, and (d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection, and pure transmission) of interaction of a moving localized mode with the defect.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.77.036614
DOI:
10.1103/PhysRevE.77.036614
PACS:
05.45.Yv, 63.20.Pw, 63.20.Ry

*Corresponding author. Permanent address: Nonlinear Physics Group, Escuela Técnica Superior de Ingeniería Informática, Departamento de Física Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012-Sevilla, Spain; palmero@us.es

 
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