Explicit solution family for the equation of the resistively shunted Josephson junction model

DOI10.1007/s11232-013-0085-2zbMath1291.34002OpenAlexW2082041785MaRDI QIDQ2449525

Victor M. Buchstaber, S. I. Tertychnyi

Publication date: 8 May 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-013-0085-2

zbMATH Keywords

rotation numberPoincaré mappolynomial solutiondouble confluent Heun equationsdynamical system on a torus

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Explicit solutions, first integrals of ordinary differential equations (34A05) Ordinary differential equations and systems on manifolds (34C40) Flows on surfaces (37E35) Rotation numbers and vectors (37E45)

Related Items (14)

On a remarkable sequence of Bessel matrices ⋮ On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation* ⋮ Solution space monodromy of a special double confluent Heun equation and its applications ⋮ On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect ⋮ On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation ⋮ On determinants of modified Bessel functions and entire solutions of double confluent Heun equations ⋮ On spectral curves and complexified boundaries of the phase-lock areas in a model of Josephson junction ⋮ Unnamed Item ⋮ Automorphisms of the solution spaces of special double-confluent Heun equations ⋮ The rotation number integer quantization effect in braid groups ⋮ Symmetries of the space of solutions to special double confluent Heun equations of integer order ⋮ Three Theorems on Vandermond Matrices ⋮ Categories of symmetry groups of the space of solutions of the special doubly confluent Heun equation ⋮ Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction

Cites Work

• Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations
• Geometry of the Prytz planimeter
• Rotation number quantization effect
• Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture
• A system on a torus modelling the dynamics of a Josephson junction
• Possible new effects in superconductive tunnelling
• On properties of the differential equation describing the dynamics of an overdamped Josephson junction
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