Dynamics of ac-driven sine-Gordon equation for long Josephson junctions with fast varying perturbation

A long Josephson junction comprising regions with phase discontinuities driven by an external ac-drive is studied. An inhomogeneous sine-Gordon equation is used, that depicts the dynamics of long Josephson junctions with phase discontinuities. Perturbation technique along with asymptotic analysis and the method of averaging are applied to obtain an average dynamics in the form of double sine-Gordon equations for both small and large driving amplitudes. From the obtained average dynamics, it is determined that, the external ac-drive may affect the presence of the ground state of the junction. Specifically, the cases for 0−κ and 0−π−0 junctions are discussed. In the presence of an external ac-drive, the critical facet length bc is analyzed for 0−π−0 junction above which the ground state is non-uniform. The critical bias current γc for 0−κ junction is investigated, at which the junction switches to a resistive state. Further, the interaction of localized defect modes and the fast oscillating drive is studied for both 0−κ and 0−π−0 junctions, which is explained by using Lagrangian approach. Numerical simulations are performed to support our analytical calculations.