Related papers: Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping

Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping

URL: http://arxiv.org/abs/2510.08781v1
Date: Thu, 09 Oct 2025 19:59:13 GMT
Title: Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
Authors: L. J. R. Bezerra Jr., W. S. Dias,
Abstract summary: We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr"odinger equation in finite square lattices.<n>We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes.<n>We identify distinct self-trapped regimes characterized by diagonal or off-diagonal localized modes, depending on the strength of $U$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes and the influence of a refractive index detuning selectively applied along the diagonal waveguides on this transition. This detuning effectively emulates the effect of on-site Hubbard-like interactions $U$ in photonic analogs of interacting particles in a one-dimensional lattice. While for $U = 0$ the system exhibits the known direct transition from stable uniform states to asymptotically localized profiles, we show that $U > 0$ induces an emergence of intermediate dynamical regimes. These regimes include coherent breathing modes that can be either confined along diagonal or off-diagonal waveguides, as well as chaotic-like propagation patterns. At higher nonlinearities, we identify distinct self-trapped regimes characterized by diagonal or off-diagonal localized modes, depending on the strength of $U$. The critical nonlinear strengths separating the existing regimes are shown in the phase diagram, underscoring the competing trends imposed by the Hubbard-like interaction on the optical field.

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