Automorphisms of the solution spaces of special double-confluent Heun equations
- 41 Downloads
Two new linear operators determining automorphisms of the solution space of a special double-confluent Heun equation in the general case are obtained. This equation has two singular points, both of which are irregular. The obtained result is applied to solve the nonlinear equation of the resistively shunted junction model for an overdamped Josephson junction in superconductors. The new operators are explicitly expressed in terms of structural polynomials, for which recursive computational algorithms are constructed. Two functional equations for the solutions of the special double-confluent Heun equation are found.
Keywordsspecial functions double-confluent Heun equation solution space automorphisms functional equations
Unable to display preview. Download preview PDF.
- R. L. Foote, M. Levi, and S. Tabachnikov, Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-Year-Old Conjecture, http://arxiv.org/abs/1207.0834v1.Google Scholar
- D. Schmidt and G. Wolf, “Double confluent Heun equation,” in: Heun’s Differential Equations (ed. by Ronveaux), Oxford Univ. Press, Oxford–New York, 1995.Google Scholar
- S. I. Tertychniy, The modelling of a Josephson junction and Heun polynomials, http://arxiv.org/abs/math-ph/0601064.Google Scholar
- The Heun Project, http://theheunproject.org/bibliography.html.Google Scholar