Grava, Tamara; Mazzuca, Guido Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation. (English) Zbl 1521.37088 Commun. Math. Phys. 399, No. 3, 1689-1729 (2023). MSC: 37K60 39A36 33C47 15B52 60B20 PDFBibTeX XMLCite \textit{T. Grava} and \textit{G. Mazzuca}, Commun. Math. Phys. 399, No. 3, 1689--1729 (2023; Zbl 1521.37088) Full Text: DOI arXiv
Tertychniy, Sergey I. Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation. (English) Zbl 1526.33006 Eur. J. Math. 8, No. 4, 1623-1654 (2022). MSC: 33E30 33C15 34M03 34M35 34M45 58D19 PDFBibTeX XMLCite \textit{S. I. Tertychniy}, Eur. J. Math. 8, No. 4, 1623--1654 (2022; Zbl 1526.33006) Full Text: DOI arXiv
Buchstaber, V. M.; Tertychnyi, S. I. Group algebras acting on the space of solutions of a special double confluent Heun equation. (English. Russian original) Zbl 1454.82051 Theor. Math. Phys. 204, No. 2, 967-983 (2020); translation from Teor. Mat. Fiz. 204, No. 2, 153-170 (2020). MSC: 82D55 81R10 34M35 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{S. I. Tertychnyi}, Theor. Math. Phys. 204, No. 2, 967--983 (2020; Zbl 1454.82051); translation from Teor. Mat. Fiz. 204, No. 2, 153--170 (2020) Full Text: DOI
Tertychniy, Sergey I. Square root of the monodromy map associated with the equation of RSJ model of Josephson junction. (English) Zbl 1459.34193 Result. Math. 75, No. 4, Paper No. 139, 36 p. (2020). Reviewer: Vladimir P. Kostov (Nice) MSC: 34M04 34M15 34M35 44A20 PDFBibTeX XMLCite \textit{S. I. Tertychniy}, Result. Math. 75, No. 4, Paper No. 139, 36 p. (2020; Zbl 1459.34193) Full Text: DOI arXiv
Tertychniy, S. I. Solution space monodromy of a special double confluent Heun equation and its applications. (English. Russian original) Zbl 1437.34087 Theor. Math. Phys. 201, No. 1, 1426-1441 (2019); translation from Teor. Mat. Fiz. 201, No. 1, 17-36 (2019). MSC: 34M03 34M35 82D55 PDFBibTeX XMLCite \textit{S. I. Tertychniy}, Theor. Math. Phys. 201, No. 1, 1426--1441 (2019; Zbl 1437.34087); translation from Teor. Mat. Fiz. 201, No. 1, 17--36 (2019) Full Text: DOI
Salatich, Alexander A.; Slavyanov, Sergey Yu. Antiquantization of the double confluent Heun equation. The Teukolsky equation. (English) Zbl 1420.34101 Russ. J. Nonlinear Dyn. 15, No. 1, 79-85 (2019). MSC: 34M03 34M35 34M55 PDFBibTeX XMLCite \textit{A. A. Salatich} and \textit{S. Yu. Slavyanov}, Russ. J. Nonlinear Dyn. 15, No. 1, 79--85 (2019; Zbl 1420.34101) Full Text: DOI MNR
Batic, D.; Mills, D.; Nowakowski, M. Semicommuting and commuting operators for the Heun family. (English. Russian original) Zbl 1401.33007 Theor. Math. Phys. 195, No. 1, 494-512 (2018); translation from Teor. Mat. Fiz. 195, No. 1, 6-26 (2018). MSC: 33C15 PDFBibTeX XMLCite \textit{D. Batic} et al., Theor. Math. Phys. 195, No. 1, 494--512 (2018; Zbl 1401.33007); translation from Teor. Mat. Fiz. 195, No. 1, 6--26 (2018) Full Text: DOI arXiv
Buchstaber, V. M.; Tertychnyi, S. I. Representations of the Klein group determined by quadruples of polynomials associated with the double confluent Heun equation. (English. Russian original) Zbl 1395.34086 Math. Notes 103, No. 3, 357-371 (2018); translation from Mat. Zametki 103, No. 3, 346-363 (2018). Reviewer: Vladimir P. Kostov (Nice) MSC: 34M03 20C05 34M15 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{S. I. Tertychnyi}, Math. Notes 103, No. 3, 357--371 (2018; Zbl 1395.34086); translation from Mat. Zametki 103, No. 3, 346--363 (2018) Full Text: DOI
Vieira, H. S. Resonant frequencies of the hydrodynamic vortex. (English) Zbl 1358.76085 Int. J. Mod. Phys. D 26, No. 4, Article ID 1750035, 9 p. (2017). MSC: 76Y05 83C57 PDFBibTeX XMLCite \textit{H. S. Vieira}, Int. J. Mod. Phys. D 26, No. 4, Article ID 1750035, 9 p. (2017; Zbl 1358.76085) Full Text: DOI arXiv
Buchstaber, V. M.; Tertychnyi, S. I. Automorphisms of the solution spaces of special double-confluent Heun equations. (English. Russian original) Zbl 1360.34176 Funct. Anal. Appl. 50, No. 3, 176-192 (2016); translation from Funkts. Anal. Prilozh. 50, No. 3, 12-33 (2016). MSC: 34M03 34M35 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{S. I. Tertychnyi}, Funct. Anal. Appl. 50, No. 3, 176--192 (2016; Zbl 1360.34176); translation from Funkts. Anal. Prilozh. 50, No. 3, 12--33 (2016) Full Text: DOI
Ishkhanyan, A. M. A singular Lambert-\(W\) Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions. (English) Zbl 1351.81041 Mod. Phys. Lett. A 31, No. 33, Article ID 1650177, 11 p. (2016). MSC: 81Q05 33C90 35J10 PDFBibTeX XMLCite \textit{A. M. Ishkhanyan}, Mod. Phys. Lett. A 31, No. 33, Article ID 1650177, 11 p. (2016; Zbl 1351.81041) Full Text: DOI arXiv
Bukhshtaber, V. M.; Tertychnyi, S. I. On a remarkable sequence of Bessel matrices. (English. Russian original) Zbl 1345.15008 Math. Notes 98, No. 5, 714-724 (2015); translation from Mat. Zametki 98, No. 5, 651-663 (2015). Reviewer: Frank Uhlig (Auburn) MSC: 15B05 34A25 33C10 PDFBibTeX XMLCite \textit{V. M. Bukhshtaber} and \textit{S. I. Tertychnyi}, Math. Notes 98, No. 5, 714--724 (2015; Zbl 1345.15008); translation from Mat. Zametki 98, No. 5, 651--663 (2015) Full Text: DOI
Buchstaber, V. M.; Tertychnyi, S. I. Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction. (English. Russian original) Zbl 1326.82028 Theor. Math. Phys. 182, No. 3, 329-355 (2015); translation from Teor. Mat. Fiz. 182, No. 3, 373-404 (2015). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 82D55 34M03 33C15 PDFBibTeX XMLCite \textit{V. M. Buchstaber} and \textit{S. I. Tertychnyi}, Theor. Math. Phys. 182, No. 3, 329--355 (2015; Zbl 1326.82028); translation from Teor. Mat. Fiz. 182, No. 3, 373--404 (2015) Full Text: DOI
Creţu, Ciprian On a Schrödinger-like equation with some special potential. (English) Zbl 1413.85007 Bul. Inst. Politeh. Iași, Secț. I, Mat. Mec. Teor. Fiz. 59(63), No. 3, 67-75 (2013). MSC: 85A40 35Q41 PDFBibTeX XMLCite \textit{C. Creţu}, Bul. Inst. Politeh. Iași, Secț. I, Mat. Mec. Teor. Fiz. 59(63), No. 3, 67--75 (2013; Zbl 1413.85007)
Abad, J.; Gómez, F. J.; Sesma, J. An algorithm to obtain global solutions of the double confluent Heun equation. (English) Zbl 1162.65041 Numer. Algorithms 49, No. 1-4, 33-51 (2008). MSC: 65L10 34B30 33E20 34M35 PDFBibTeX XMLCite \textit{J. Abad} et al., Numer. Algorithms 49, No. 1--4, 33--51 (2008; Zbl 1162.65041) Full Text: DOI arXiv
Tertychniy, Sergey I. General solution of overdamped Josephson junction equation in the case of phase-lock. (English) Zbl 1132.33341 Electron. J. Differ. Equ. 2007, Paper No. 133, 20 p. (2007). MSC: 33E30 34A05 34A25 34B30 34B60 34M05 34M35 70K40 PDFBibTeX XMLCite \textit{S. I. Tertychniy}, Electron. J. Differ. Equ. 2007, Paper No. 133, 20 p. (2007; Zbl 1132.33341) Full Text: arXiv EuDML EMIS
Hounkonnou, Mahouton Norbert; Ronveaux, André; Sodoga, Komi Factorization of some confluent Heun’s differential equations. (English) Zbl 1126.34307 Appl. Math. Comput. 189, No. 1, 816-820 (2007). MSC: 34A30 47E05 PDFBibTeX XMLCite \textit{M. N. Hounkonnou} et al., Appl. Math. Comput. 189, No. 1, 816--820 (2007; Zbl 1126.34307) Full Text: DOI
Wolf, Gerhard On the central connection problem for the double confluent Heun equation. (English) Zbl 0919.34007 Math. Nachr. 195, 267-276 (1998). Reviewer: N.V.Grigorenko (Kyïv) MSC: 34M40 34A30 34E05 PDFBibTeX XMLCite \textit{G. Wolf}, Math. Nachr. 195, 267--276 (1998; Zbl 0919.34007) Full Text: DOI
Kazakov, A. Ya.; Slavyanov, S. Yu. Integral equations for special functions of Heun class. (English) Zbl 0883.34029 Methods Appl. Anal. 3, No. 4, 447-456 (1996). Reviewer: R.S.Dahiya (Ames) MSC: 34B30 33C99 34A25 PDFBibTeX XMLCite \textit{A. Ya. Kazakov} and \textit{S. Yu. Slavyanov}, Methods Appl. Anal. 3, No. 4, 447--456 (1996; Zbl 0883.34029) Full Text: DOI
Bühring, Wolfgang The double confluent Heun equation: Characteristic exponent and connection formulae. (English) Zbl 0849.34004 Methods Appl. Anal. 1, No. 3, 348-370 (1994). MSC: 34M99 34A30 34E05 PDFBibTeX XMLCite \textit{W. Bühring}, Methods Appl. Anal. 1, No. 3, 348--370 (1994; Zbl 0849.34004) Full Text: DOI
Schmidt, Dieter; Wolf, Gerhard On the double confluent Heun equation. (English) Zbl 0902.34002 Alavi, Yousev (ed.) et al., Trends and developments in ordinary differential equations. Proceedings of the international symposium, Kalamazoo, MI, USA, May 20-22, 1993. Singapore: World Scientific. 293-303 (1994). Reviewer: J.Schmeelk (Richmond) MSC: 34M99 PDFBibTeX XMLCite \textit{D. Schmidt} and \textit{G. Wolf}, in: Trends and developments in ordinary differential equations. Proceedings of the international symposium, Kalamazoo, MI, USA, May 20-22, 1993. Singapore: World Scientific. 293--303 (1994; Zbl 0902.34002)
Exton, H. The doubly confluent Heun equation: A differential equation associated with the naked singularity in cosmology. (English) Zbl 0756.34010 Rend. Mat. Appl., VII. Ser. 11, No. 4, 905-911 (1991). Reviewer: J.Schmeelk (Richmond) MSC: 34A30 34A25 34M35 34B30 85A40 PDFBibTeX XMLCite \textit{H. Exton}, Rend. Mat. Appl., VII. Ser. 11, No. 4, 905--911 (1991; Zbl 0756.34010)