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

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.

arXiv comment12 pages, 10 figures

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Cited by in corpus (8)

• Interface solitons in one-dimensional locally-coupled lattice systems
• Interaction of discrete nonlinear Schrödinger solitons with a linear lattice impurity
• Lower and upper estimates on the excitation threshold for breathers in DNLS lattices
• Interface solitons in locally linked two-dimensional lattices
• Breather solutions of the discrete p-Schrödinger equation
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Structure of Noncommutative Solitons: Existence and Spectral Theory
• Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates