General solution of overdamped Josephson junction equation in the case of phase-lock

TL;DR

This paper derives the general solution for an overdamped Josephson junction equation in phase-lock mode, using Floquet solutions of the double confluent Heun equation, advancing understanding of nonlinear Josephson dynamics.

Contribution

It provides the first explicit general solution for the nonlinear Josephson junction equation in phase-lock conditions, expressed via Floquet solutions of a special function.

Findings

Solution expressed in terms of Floquet solutions of the double confluent Heun equation

Analytical description of phase-lock mode in overdamped Josephson junctions

Enhanced understanding of nonlinear dynamics in Josephson systems

Abstract

The first order nonlinear ODE d phi(t)/d t + sin phi(t)=B+A cos(omega t), (A,B,omega are real constants) is investigated. Its general solution is derived in the case of the choice of parameters ensuring the phase-lock mode. It is represented in terms of Floquet solution of double confluent Heun equation.