Families of Discrete Breathers on a Nonlinear Kagome Lattice

TL;DR

This paper investigates the existence, properties, and stability of discrete breathers in a nonlinear Kagome lattice, revealing new stable localized modes and their energy thresholds near the linear spectrum edges.

Contribution

It provides the first detailed analysis of discrete breathers on a Kagome lattice, including conditions for existence, explicit solutions, and stability characteristics.

Findings

Existence of stable breathers inside the band gap.

Explicit compactly supported breather solutions.

Asymptotic energy thresholds in the weakly nonlinear regime.

Abstract

The unique geometry of the two-dimensional tripartite Kagome lattice is responsible for shaping diverse families of spatially localized and time-periodic nonlinear modes known as discrete breathers. We state conditions for the existence of breathers and compute their spatiotemporal profiles near the edges of the linear phonon spectrum. Our findings include the existence of strongly nonlinear and dynamically stable breathers inside the band gap on the infinite lattice, asymptotic expressions for breather energy thresholds in the weakly nonlinear regime, and explicit breather solutions that remain compactly supported on the lattice and undergo stability transitions.