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The modelling of a Josephson junction and Heun polynomials
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The first order nonlinear ODE \dot \phi(t) + \sin\phi(t)=q(t),q(t)=B+A\cos\omega t, where A,B,\omega are real constants, is considered, the transformation converting it to a second order linear homogeneous ODE with polynoimial coefficients is found. The latter is identified as a particular case of the double confluent Heun equation. The series of algebraic constraints on the constant parameters is found whose fulfillment leads to the existance of solutions representable through polynomials in explicit form. These polynomials are found to constitute the orthogonal normalizable system
Forward citations
Cited by 2 Pith papers
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On phase-lock area parquet in a special slow-fast limit of model of Josephson junction
In the slow-fast limit, the phase-lock areas of the RSJ Josephson junction model converge to a parquet of integer-spaced squares/strips with boundaries parallel to u±ℓ=0.
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Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking
A deformed RSJ model related to general Heun equations keeps integer-only phase-lock areas while breaking all constrictions.
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