Thresholdless nonlinearity-induced edge solitons in trimer arrays

Abstract

We consider a one-dimensional discrete nonlinear Schrödinger (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.

6 pages, 5 figures, to be published in Low Temperature Physics, Special Issue dedicated to the 80th birthday of Alexander Kovalev

References in corpus (4)

• Observation of edge solitons in topological trimer arrays
• Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model
• Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators
• Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential