Nonlinear skin modes and fixed points

• URL: http://arxiv.org/abs/2411.12424v3
• Date: Tue, 04 Feb 2025 04:10:48 GMT
• Title: Nonlinear skin modes and fixed points
• Authors: C. Yuce,
• Abstract summary: We investigate a one-dimensional tight-binding lattice with asymmetrical couplings and various type of nonlinearities to study nonlinear non-Hermitian skin effect. The nonlinear interactions are shown to have no impact on the spectral region in the semi-infinite system. We identify distinctive features of nonlinear skin modes, such as degeneracy, and power-energy discontinuity.
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• Abstract: We investigate a one-dimensional tight-binding lattice with asymmetrical couplings and various type of nonlinearities to study nonlinear non-Hermitian skin effect. Our focus is on the exploration of nonlinear skin modes through a fixed-point perspective. The nonlinear interactions are shown to have no impact on the spectral region in the semi-infinite system; however, they induce considerable changes when boundaries are present. The spectrum under open boundary conditions is found not to be a subset of the corresponding spectrum under the semi-infinite boundary conditions. We identify distinctive features of nonlinear skin modes, such as degeneracy, and power-energy discontinuity. Furthermore, we demonstrate that a family of localized modes that are neither skin nor scale-free localized modes is formed with the introduction of a coupling impurity. Additionally, we show that an impurity can induce discrete dark and anti-dark solitons.

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