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arXiv · 0712.2322

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

F. Palmero·R. Carretero-González·J. Cuevas·P. G. Kevrekidis·W. Królikowski
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Abstract

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.

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F. Palmero, R. Carretero-González, J. Cuevas, P. G. Kevrekidis, W. Królikowski. 2007-12-14. Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity. https://doi.org/10.1103/physreve.77.036614

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