Kinks in the parametrically excited sine-Gordon equation and method of averaging

TL;DR

This paper investigates the parametrically excited sine-Gordon equation using averaging methods, revealing kink solutions that model phenomena like Bloch wall movement and fluxon dynamics in Josephson junctions.

Contribution

It introduces an averaging technique for the excited sine-Gordon equation, enabling analysis of kink solutions under various excitation amplitudes.

Findings

Averaged equations admit kink solutions.

Applications to ferromagnetic Bloch walls.

Modeling fluxon dynamics in Josephson junctions.

Abstract

Parametrically excited sine-Gordon equation is considered. Excitation is a fast oscillating periodic function with zero mean. Technique of classical method of averaging enables to construct the averaged equations in a variety of assumptions about driving amplitude. The averaged equation possesses kinks solutions. The results can be applied to the study of movement of Bloch walls for ferromagnetic crystals in the presence of a rapidly oscillating magnetic field and to describe the fluxon dynamics in long Josephson junctions.