Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment

TL;DR

This paper investigates the existence, stability, and formation of discrete breathers in a nonlinear electric ring, combining experimental, numerical, and theoretical approaches to understand their behavior and conditions for emergence.

Contribution

It presents a comprehensive study of discrete breathers in a nonlinear electric line, including modeling, stability analysis, experimental validation, and insights into spontaneous formation mechanisms.

Findings

Discrete breathers exist in specific voltage and frequency regions.

Good quantitative agreement between experiments and simulations.

Modulational instability leads to spontaneous formation of breathers.

Abstract

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.