Breathers in lattices with alternating strain-hardening and strain-softening interactions

TL;DR

This paper investigates the existence, stability, and bifurcation of breathers in a nonlinear lattice with alternating strain-hardening and strain-softening interactions, analyzing effects of damping, driving, and deriving NLS equations.

Contribution

It introduces a systematic study of breathers in such lattices, including analytical derivation of NLS equations and comparison with numerical solutions, highlighting new insights into nonlinear lattice dynamics.

Findings

Linear resonant peaks bend toward the frequency gap with nonlinearity.

Time-periodic solutions within the gap resemble Hamiltonian breathers with small damping and driving.

Derived NLS equations accurately predict acoustic and optical breathers in the Hamiltonian limit.

Abstract

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a Nonlinear Schr\"odinger (NLS) equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.