Inductive intrinsic localized modes in a 1D nonlinear electric transmission line

TL;DR

This paper demonstrates the existence of a new type of intrinsic localized mode (ILM) in a 1D nonlinear electrical transmission line with nonlinear inductance, showing how ILMs can exist outside the plane wave spectrum and connecting lattice defect dynamics to ILMs.

Contribution

It introduces a novel ILM in a 1D nonlinear electrical lattice with nonlinear inductance and provides analytic and numerical analysis of its properties.

Findings

ILMs exist outside the plane wave spectrum.

Current ILMs are spatially compressed compared to flux ILMs.

Analytic results agree with simulations and eigenvalue analysis.

Abstract

The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D lumped electrical transmission line a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis the nonlinear inductive current equations are transformed to flux transmission line equations with analogue onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.