Lower and upper estimates on the excitation threshold for breathers in DNLS lattices

TL;DR

This paper derives analytical lower and upper bounds for the energy threshold needed to excite breathers in DNLS lattices, aiding in understanding localized oscillations in nonlinear lattice systems.

Contribution

It introduces explicit analytical estimates for breather excitation thresholds in DNLS lattices based on lattice parameters and frequency, validated by numerical studies.

Findings

Analytical bounds effectively predict breather activation energy.

Estimates depend explicitly on lattice parameters and solution frequency.

Numerical results confirm the usefulness of the bounds for detection.

Abstract

We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized and time periodic solutions) in DNLS lattices with power nonlinearity. The estimation depending explicitly on the lattice parameters, is derived by a combination of a comparison argument on appropriate lower bounds depending on the frequency of each solution with a simple and justified heuristic argument. The numerical studies verify that the analytical estimates can be of particular usefulness, as a simple analytical detection of the activation energy for breathers in DNLS lattices.