Thresholdless nonlinearity-induced edge solitons in trimer arrays
Abstract
We consider a one-dimensional discrete nonlinear Schr\"odinger (DNLS) model with Kerr-type on-site nonlinearity, where the nearest-neighbor coupling constants take two different values ordered in a three-periodic sequence. The existence of localized edge states in the linear limit (Su-Schrieffer-Heeger trimer, SSH3) is known to depend on the precise location of the edge. Here, we show that for a termination that does not support linear edge states, an arbitrarily weak on-site nonlinearity will induce an edge mode with asymptotic exponential localization, bifurcating from a linear band edge. Close to the gap edge, the shape of the mode can be analytically described in a continuum approximation as one half of a standard gap soliton. The linear stability properties of nonlinear edge modes are also discussed.
Cite
@article{arxiv.2502.19330,
title = {Thresholdless nonlinearity-induced edge solitons in trimer arrays},
author = {Magnus Johansson},
journal= {arXiv preprint arXiv:2502.19330},
year = {2025}
}
Comments
6 pages, 5 figures, to be published in Low Temperature Physics, Special Issue dedicated to the 80th birthday of Alexander Kovalev