Floquet breathers in a modulated nonlinear lattice

TL;DR

This paper investigates Floquet breathers in a space-time modulated nonlinear lattice, revealing diverse breather types and stability behaviors influenced by modulation frequency, with potential applications in dynamic metamaterials.

Contribution

It extends the theory of breather existence and stability to include space-time modulation in a nonlinear lattice system, supported by numerical simulations.

Findings

Identified three types of breather responses depending on the driving frequency.

Demonstrated the existence of various breather configurations, including site-centered and bond-centered.

Analyzed stability evolution of breathers as a function of modulation frequency.

Abstract

In this work, we study a space-time modulated electro-mechanical system, consisting of an array of coupled cantilevers with their on-site potential provided by electromagnets driven by AC currents. Model equations are derived, and the effect of the modulation on the dispersion bands is examined. The theory of breather existence and stability is extended to include space-time modulation. We perform numerical simulations in a time-modulated system, showing three types of breather response depending on the driving frequency: (i) the modulation frequency is an integer multiple of the breather frequency or, in other words, this phenomenon corresponds to period doubling, tripling, etc.; (ii) the opposite, that is, the breather frequency is an integer multiple of the modulation frequency, corresponding to period-halving, etc. (iii) the breather and modulation frequencies are commensurate in a different form. We use for all of them the term {\em Floquet breathers} in analogy with Floquet solitons in photonic systems. As there is no dissipation, but periodic forcing, the energy is generally conserved but only at discrete times. There exists in this system a huge variety of breathers, either site-centered, symmetric and antisymmetric, bond centered, in-phase or in-quadrature with the modulation, and we analyze the evolution of stability of some of them as a function of the modulation frequency. The construction of a similar system would be of interest to study the properties of dynamic metamaterials.