Abstract:
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.
Citation:
V. M. Buchstaber, S. I. Tertychnyi, “Automorphisms of the solution spaces of special double-confluent Heun equations”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 12–33; Funct. Anal. Appl., 50:3 (2016), 176–192
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\paper Automorphisms of the solution spaces of special double-confluent Heun equations
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\jour Funct. Anal. Appl.
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\vol 50
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https://doi.org/10.4213/faa3245
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This publication is cited in the following 13 articles:
Alexey A. Glutsyuk, “Extended Model of Josephson Junction, Linear Systems with Polynomial Solutions, Determinantal Surfaces, and Painlevé III Equations”, Proc. Steklov Inst. Math., 326 (2024), 90–132
Sergey I. Tertychniy, “Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation”, European Journal of Mathematics, 8:4 (2022), 1623
Y Bibilo, A A Glutsyuk, “On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation*”, Nonlinearity, 35:10 (2022), 5427
V. M. Buchstaber, S. I. Tertychnyi, “Categories of Symmetry Groups of the Space of Solutions of the Special Doubly Confluent Heun Equation”, Math. Notes, 110:5 (2021), 643–654
V. M. Buchstaber, S. I. Tertychnyi, “Group algebras acting on the space of solutions of a special double
confluent Heun equation”, Theoret. and Math. Phys., 204:2 (2020), 967–983
S. I. Tertychniy, “Square root of the monodromy map associated with the equation of rsj model of Josephson junction”, Results Math., 75:4 (2020), 139
Glutsyuk A.A., Netay I.V., “On Spectral Curves and Complexified Boundaries of the Phase-Lock Areas in a Model of Josephson Junction”, J. Dyn. Control Syst., 26:4 (2020), 785–820
A. A. Glutsyuk, “On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation”, J. Dyn. Control Syst., 25:3 (2019), 323–349
A. V. Malyutin, “The Rotation Number Integer Quantization Effect in Braid Groups”, Proc. Steklov Inst. Math., 305 (2019), 182–194
S. I. Tertychnyi, “Solution space monodromy of a special double confluent Heun equation and its applications”, Theoret. and Math. Phys., 201:1 (2019), 1426–1441
S. I. Tertychniy, “Symmetries of the space of solutions to special double confluent Heun equations of integer order”, J. Math. Phys., 60:10 (2019), 103501
V. M. Buchstaber, S. I. Tertychnyi, “Representations of the Klein Group
Determined by Quadruples of Polynomials
Associated with the Double Confluent Heun Equation”, Math. Notes, 103:3 (2018), 357–371
V. M. Buchstaber, A. A. Glutsyuk, “On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect”, Proc. Steklov Inst. Math., 297 (2017), 50–89
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