Supertransmission channel for an intrinsic localized mode in a 1D nonlinear physical lattice

TL;DR

This paper investigates how the resonance between a moving intrinsic localized mode (ILM) and the lattice's normal modes can be controlled through nonlinearities, enabling supertransmission in a 1D nonlinear lattice.

Contribution

It introduces a Fourier transform analysis of the nonlinear force to quantify and control resonance, revealing a supertransmission channel for ILMs in nonlinear lattices.

Findings

Resonance strength depends on the mix of onsite and intersite nonlinearities.

Engineering nonlinearity mix can greatly reduce resonance.

Supertransmission channel enables ILM propagation without energy loss.

Abstract

It is well known that a moving intrinsic localized mode (ILM) in a nonlinear physical lattice looses energy because of the resonance between it and the underlying small amplitude plane wave spectrum. By exploring the Fourier transform (FT) properties of the nonlinear force of a running ILM in a driven and damped 1D nonlinear lattice, as described by a 2-D wavenumber and frequency map, we quantify the magnitude of the resonance where the small amplitude normal mode dispersion curve and the FT amplitude components of the ILM intersect. We show that for a traveling ILM characterized by a specific frequency and wavenumber, either inside or outside the plane wave spectrum, and for situations where both onsite and intersite nonlinearity occur, either of the hard or soft type, the strength of this resonance depends on the specific mix of the two nonlinearities. Examples are presented demonstrating that by engineering this mix the resonance can be greatly reduced. The end result is a supertransmission channel for either a driven or undriven ILM in a nonintegrable, nonlinear yet physical lattice.