Discrete Breathers in a Nonlinear Polarizability Model of Ferroelectrics

TL;DR

This paper introduces a family of discrete breathers in a nonlinear polarizability model of ferroelectrics, demonstrating their existence, bifurcation behavior, and stability through numerical analysis and simulations.

Contribution

It provides the first detailed numerical and bifurcation analysis of discrete breathers in a nonlinear ferroelectric model, including stability and phantom breather phenomena.

Findings

Discrete breathers exist in the spectral gap of the model.

Breathers bifurcate from nonlinear normal modes.

Numerical simulations reveal stability and instability regimes.

Abstract

We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its non-dimensionalized Hamiltonian form and its linear spectrum is examined. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises.