Modulated harmonic wave in series connected discrete Josephson transmission line: the discrete calculus approach

TL;DR

This paper develops a discrete calculus approach to analyze modulated harmonic waves in Josephson transmission lines, deriving a nonlinear Schrödinger equation to describe soliton behavior, validated through comparison with previous results.

Contribution

It introduces a novel discrete calculus method for modulation analysis in discrete wave systems, specifically applied to Josephson transmission lines.

Findings

Derivation of a discrete NLS equation for JTL modulation

Validation of the approach with Fermi-Pasta-Ulam-Tsingou problem

Comparison of soliton profiles with previous results

Abstract

We consider the modulated harmonic wave in the discrete series connected Josephson transmission line (JTL). We formulate the approach to the modulation problems for discrete wave equations based on discrete calculus. We check up the approach by applying it to the Fermi-Pasta-Ulam-Tsingou type problem. Applying the approach to the discrete JTL, we obtain the equation describing the modulation amplitude, which turns out to be the defocusing nonlinear Schr\"odinger (NLS) equation. We compare the profile of the single soliton solution of the NLS with that of the soliton obtained in our previous publication.