NDLI: Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction

Content Provider	Springer Nature Link
Author	Buchstaber, V. M. Tertychnyi, S. I.
Copyright Year	2015
Abstract	This work is a continuation of research on a first-order nonlinear differential equation applied in the overshunted model of the Josephson junction. The approach is based on the relation between this equation and the double confluent Heun equation, which is a second-order linear homogeneous equation with two irregular singular points. We describe the conditions on the equation parameters under which its general solution is an analytic function on the Riemann sphere except at 0 and ∞. We construct an explicit basis of the solution space. One of the functions in this basis is regular everywhere except 0, and the other is regular everywhere except ∞. We show that in the framework of the RSJ model of Josephson junction dynamics, the described situation corresponds to the condition that the Shapiro step vanishes if all the solutions of the double confluent Heun equation are single-valued on the Riemann sphere without 0 and ∞.
Starting Page	329
Ending Page	355
Page Count	27
File Format	PDF
ISSN	00405779
Journal	Theoretical and Mathematical Physics
Volume Number	182
Issue Number	3
e-ISSN	15739333
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-04-08
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	double confluent Heun equation holomorphic solution dynamical system on a torus with the identical Poincaré map Theoretical, Mathematical and Computational Physics Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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