PreprintCC BY 4.0arXiv
Discrete PT-symmetric solitons on branched lattices: Vertex states, stability, and vortices
Abstract
Branching fundamentally modifies nonlinear localization by introducing vertex degrees of freedom absent in one-dimensional lattices. We investigate localized states in a PT-symmetric four-edge star graph described by the discrete nonlinear Schrödinger equation. We identify a discrete vortex state with a fixed topological charge, supported by the branching geometry. Constructed by continuation from the anticontinuum limit, the vortex evolves into a current-carrying state in the presence of balanced gain and loss and exhibits stability windows absent for the conventional branches. A possible electric-circuit realization of the proposed model is discussed.
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BibTeX
@misc{akramov2026discrete,
title = {{Discrete PT-symmetric solitons on branched lattices: Vertex states, stability, and vortices}},
author = {M. Akramov and A. Fayzullaev and O. Tojakhmadova and T. Akhmadjanov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00774},
eprint = {2610.00774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00774},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discrete PT-symmetric solitons on branched lattices: Vertex states, stability, and vortices
AU - M. Akramov
AU - A. Fayzullaev
AU - O. Tojakhmadova
AU - T. Akhmadjanov
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00774
UR - https://arxiv.org/abs/2610.00774
AB - Branching fundamentally modifies nonlinear localization by introducing vertex degrees of freedom absent in one-dimensional lattices. We investigate localized states in a PT-symmetric four-edge star graph described by the discrete nonlinear Schrödinger equation. We identify a discrete vortex state with a fixed topological charge, supported by the branching geometry. Constructed by continuation from the anticontinuum limit, the vortex evolves into a current-carrying state in the presence of balanced gain and loss and exhibits stability windows absent for the conventional branches. A possible electric-circuit realization of the proposed model is discussed.
ER -