The modelling of a Josephson junction and Heun polynomials

Details The modelling of a Josephson junction and Heun polynomials The modelling of a Josephson junction and Heun polynomials

2006-01-30

arxiv.org/abs/math-ph/0601064v1

Physics

Mathematical Physics

8 pages

Scientific paper

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

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