Thresholdless nonlinearity-induced edge solitons in trimer arrays

Magnus Johansson

doi:10.1063/10.0036750

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arXiv · 2502.19330

Thresholdless nonlinearity-induced edge solitons in trimer arrays

Magnus Johansson

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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.

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Magnus Johansson. 2025-02-26. Thresholdless nonlinearity-induced edge solitons in trimer arrays. https://doi.org/10.1063/10.0036750

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