Article
Standing and traveling waves in a model of periodically modulated one-dimensional waveguide arrays
Author/s | Parker, Ross
Aceves, Alejandro Cuevas-Maraver, Jesús Kevrekidis, Panayotis G. |
Department | Universidad de Sevilla. Departamento de Física Aplicada I |
Publication Date | 2023-08 |
Deposit Date | 2024-05-10 |
Abstract | In the present work we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial ... In the present work we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high-power initial conditions yield stationary solutions. We explain these two behaviors, as well as the nature of the transition between the two regimes, by analyzing a simpler model where the couplings between waveguides are given by step functions. For the original model, we numerically construct both stationary and moving coherent structures, which are solutions reproducing themselves exactly after an integer multiple of the coupling period. For the stationary solutions, which are true periodic orbits, we use Floquet analysis to determine the parameter regime for which they are spectrally stable. Typically, the traveling solutions are characterized by having small-amplitude oscillatory tails, although we identify a set of parameters for which these tails disappear. These parameters turn out to be independent of the lattice size, and our simulations suggest that for these parameters, numerically exact traveling solutions are stable. |
Funding agencies | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Junta de Andalucía Ministerio de Ciencia e Innovación (MICIN). España |
Project ID. | US-1380977
PID2019-110430GB-C21 PID2020-112620GB-I00 |
Files | Size | Format | View | Description |
---|---|---|---|---|
PRe_cuevas-maraver_2023_standi ... | 2.302Mb | [PDF] | View/ | |
This item appears in the following collection(s)
This document is protected by intellectual and industrial property rights. Without prejudice to existing legal exemptions, its reproduction, distribution, public communication or transformation is prohibited without the authorization of the rights holder, unless otherwise indicated.