Publication Date
2022
Journal or Book Title
arXiv Preprint
Abstract
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 bandgap 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 solitary wave setting into motion due to the instability.
DOI
https://doi.org/10.48550/arXiv.2212.02134
License
UMass Amherst Open Access Policy
Recommended Citation
Chaunsali, Rajesh; Kevrekidis, Panayotis G.; Frantzeskakis, Dimitri; and Theocharis, Georgios, "Dirac Solitons and Topological Edge States in the β-Fermi-Pasta-Ulam-Tsingou dimer lattice" (2022). arXiv Preprint. 1330.
https://doi.org/10.48550/arXiv.2212.02134