Stability of intersite dark solitons in a parametrically driven discrete nonlinear Schrödinger equation

Abstract

In this paper, a parametrically driven discrete nonlinear Schrödinger equation will be considered for defocusing case. Analytical and numerical calculations will be performed to determine the existence and stability of intersite dark discrete solitons admitted by discrete nonlinear Schrödinger equation. It will be shown that a parametric driving can stabilizes intersite discrete dark solitons. Stability windows of all the fundamental solitons will be presented and approximations to the onset of instability will be derived using perturbation theory, with accompanying numerical results.

Generation and Propagation of Topological Solitons in a Chain of Coupled Parametric-Micromechanical-Resonator Arrays

“…They correspond to the phase boundary between two parametric-oscillation states (see Fig. 1) and a continuous version of a dark soliton obtained in [39] and [40] for small coupling lim 𝑥→±∞ 𝑠(𝑥, 𝑡) = ±𝜌 0 , lim 𝑥→±∞ 𝑐(𝑥, 𝑡) = 0.…”

“…Reflecting the recent progress of device-fabrication technology, interest in a "coupled mechanical-resonator array" has been increasing. Devices comprising a large number of micro-and nano-electromechanical systems are routinely fabricated, and peculiar collective behaviors, such as mode localization and synchronization, have been studied both theoretically and experimentally [25] - [40] . Among those behaviors, intrinsic localized modes (ILMs), also known as lattice solitons, have been studied [26] , [32] - [40] .…”

“…Devices comprising a large number of micro-and nano-electromechanical systems are routinely fabricated, and peculiar collective behaviors, such as mode localization and synchronization, have been studied both theoretically and experimentally [25] - [40] . Among those behaviors, intrinsic localized modes (ILMs), also known as lattice solitons, have been studied [26] , [32] - [40] . A parametric-resonator array has also been extensively studied and well-described in the rotating frame by using the so-called "parametrically driven nonlinear Schrodinger equation" (PNSE) [32] - [40] , which was shown to have solitons as solutions.…”

“…Among those behaviors, intrinsic localized modes (ILMs), also known as lattice solitons, have been studied [26] , [32] - [40] . A parametric-resonator array has also been extensively studied and well-described in the rotating frame by using the so-called "parametrically driven nonlinear Schrodinger equation" (PNSE) [32] - [40] , which was shown to have solitons as solutions. However, the study of topological solitons in a parametric-resonator array is limited, and, to the best of my knowledge, only the stability of a static dark soliton has been discussed [39] [40] .…”

“…A parametric-resonator array has also been extensively studied and well-described in the rotating frame by using the so-called "parametrically driven nonlinear Schrodinger equation" (PNSE) [32] - [40] , which was shown to have solitons as solutions. However, the study of topological solitons in a parametric-resonator array is limited, and, to the best of my knowledge, only the stability of a static dark soliton has been discussed [39] [40] . As in the case of other topological edge states, a topological soliton is a kind of topological defect between two different phase domains, and is a commonly observed excitation in one-dimensional systems with discontinuous symmetry breaking [41] .…”