Solitons in a modified discrete nonlinear Schroedinger equation

Mario I. Molina

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arXiv · 1708.06045

Solitons in a modified discrete nonlinear Schroedinger equation

Mario I. Molina

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Abstract

We study the bulk and surface nonlinear modes of the modified one-dimensional discrete nonlinear Schroedinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls- Nabarro barrier, facilitating in this way a degree of steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The similarity of all these results to the ones obtained for the DNLS equation, points out to the robustness of the discrete soliton phenomenology.

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Mario I. Molina. 2017-08-21. Solitons in a modified discrete nonlinear Schroedinger equation. https://arxiv.org/abs/1708.06045

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