Periodic solutions of a resistive model for nonlocal Josephson dynamics

TL;DR

This paper introduces a new method for deriving periodic solutions in a nonlocal Josephson electrodynamics model, revealing steady asymptotic profiles independent of initial conditions.

Contribution

The authors develop a novel approach that reduces the model to linear ODEs, enabling explicit construction of periodic solutions in nonlocal Josephson dynamics.

Findings

Periodic solutions are explicitly constructed using trigonometric functions.

Large time asymptotics show solutions tend to a steady profile.

Steady profiles are independent of initial conditions.

Abstract

A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a sequence of nonlinear transformations. The periodic solutions are then obtained by a standard procedure which are represented in terms of trigonometric functions. It is found that the large time asymptotic of the solution exhibits a steady profile which does not depend on initial conditions.