Dynamics of ac-driven sine-Gordon equation for long Josephson junctions with fast varying perturbation. (February 2018)

• Record Type: Journal Article
• Authors: Gul, Zamin; Ali, Amir; Ahmad, Irshad
• Is Part Of: Chaos, solitons and fractals. Volume 107(2018)
• Page Start: 103
• Page End: 110
• Publication Date: 2018-02
• Subjects: Long Josephson junctions -- Rapidly oscillating ac-drive -- Method of averaging -- Perturbation techniques -- Multiple-scale analysis -- Sine-Gordon equation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.12.025
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: An inhomogeneous sine-Gordon equation is considered to study the dynamics of long Josephson junctions with phase shifts driven by an external ac-drive. Perturbation techniques together with asymptotic analysis are applied to obtain an average dynamics in the form of double sine-Gordon equations for small and large driving amplitudes. From the obtained average dynamics, it is determined that, the external drive may affect the presence of the ground state of the junction. In the presence of external drive, the critical facet length for junction and the critical bias current for junction are discussed. The interaction of localized defect modes and the fast oscillating ac-drive is studied, which is explained by using Lagrangian approach. Abstract: 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.