Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

Rita I Babicheva; Alexander S Semenov; Elvira G Soboleva; Aleksey A Kudreyko; Kun Zhou; Sergey V Dmitriev

doi:10.1103/PhysRevE.103.052202

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

Phys Rev E. 2021 May;103(5-1):052202. doi: 10.1103/PhysRevE.103.052202.

Authors

Rita I Babicheva¹, Alexander S Semenov², Elvira G Soboleva³, Aleksey A Kudreyko⁴, Kun Zhou⁵, Sergey V Dmitriev^{6

7}

Affiliations

¹ School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore.
² Polytechnic Institute (Branch) in Mirny, North-Eastern Federal University, Tikhonova St. 5/1, 678170 Mirny, Sakha Republic (Yakutia), Russia.
³ Yurga Institute of Technology (Branch), National Research Tomsk Polytechnic University, 652050 Yurga, Russia.
⁴ Department of Medical Physics and Informatics, Bashkir State Medical University, Lenin St. 3, 450008 Ufa, Russia.
⁵ Environmental Process Modelling Centre, Nanyang Environment & Water Research Institute, Nanyang Technological University, 1 Cleantech Loop, Singapore 637141, Singapore.
⁶ Institute for Metals Superplasticity Problems of RAS, Khalturin St. 39, Ufa 450000, Russia.
⁷ Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of RAS, Oktyabrya Ave. 151, Ufa 450075, Russia.

PMID: 34134260
DOI: 10.1103/PhysRevE.103.052202

Abstract

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular β-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular β-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.