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

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Abstract

We obtain and study a family of solutions of the equation \(\dot \varphi \) + sin ϕ = B + A cos ωt, which is applicable to several problems in physics, mechanics, and geometry. We use polynomial solutions of double confluent Heun equations associated with this equation to construct the family. We describe the manifold M P of parameters (A,B, ω) of these solutions and obtain explicit formulas for the rotation number and Poincaré map of the dynamical system on a torus corresponding to this equation with parameters (A,B, ω) ∈ M P .

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    V. M. Buchstaber

  2. All-Russian Scientific Research Institute of Physical-Technical and Radiotechnical Measurements, Mendeleevo, Moscow Oblast, Russia

    S. I. Tertychniy

Authors
  1. V. M. Buchstaber
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  2. S. I. Tertychniy
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Correspondence to V. M. Buchstaber.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 176, No. 2, pp. 163–188, August 2013.

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Buchstaber, V.M., Tertychniy, S.I. Explicit solution family for the equation of the resistively shunted Josephson junction model. Theor Math Phys 176, 965–986 (2013). https://doi.org/10.1007/s11232-013-0085-2

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