This paper investigates the triplet of linear operators that determines automorphisms of the set of solutions to special double confluent Heun equations of integer order. Their pairwise composition rules are computed in explicit form. It is shown that, under the conditions motivated by physical applications, these operators generate the group of symmetries of the linear space of solutions that is isomorphic to the dihedral group, provided the monodromy equivalence relation is applied. On the corresponding projective space, the symmetry group reduces to the Klein group. The results presented in this paper have implications for the modeling of Josephson junctions.

Topics
Superconducting devices, Algebraic structures, Functional equations, Group theory, Operator theory, Functions and mappings, Complex analysis, Complex functions
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27.

The analogous codes handling L-operators defined by Eqs. (20)–(22) and (26) are available from the author on request.

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See https://reference.wolfram.com/language/ for Wolfram Language & System (referred to April 03, 2019).
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2019
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