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Dirac solitons and topological edge states in the β -Fermi-Pasta-Ulam-Tsingou dimer lattice

Chaunsali, R and Kevrekidis, PG and Frantzeskakis, D and Theocharis, G (2023) Dirac solitons and topological edge states in the β -Fermi-Pasta-Ulam-Tsingou dimer lattice. In: Physical Review E, 108 (5).

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Official URL: https://doi.org/10.1103/PhysRevE.108.054224


We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference and the cubic nonlinearity (β-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice band gap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model's conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be glued to the boundaries for different types of boundary conditions. We thus explain the existence of various kinds of nonlinear edge states in the system, of which only one leads to the standard topological edge states observed in the linear limit. We finally examine the stability of bulk and edge states and verify them through direct numerical simulations, in which we observe a solitonlike wave setting into motion due to the instability. © 2023 American Physical Society.

Item Type: Journal Article
Publication: Physical Review E
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to American Physical Society.
Keywords: Energy gap; Topology, reductions; Bulk state; Conservation law; Cubic nonlinearities; Edge state; Finite domains; Linear-coupling; Soliton solutions; Type systems; Weakly non-linear, Solitons
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 29 Feb 2024 06:21
Last Modified: 29 Feb 2024 06:21
URI: https://eprints.iisc.ac.in/id/eprint/83743

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