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Modern Physics Letters A, ISSN 0217-7323, 08/2019, Volume 34, Issue 24, p. 1950195
Analytical solutions of the Schrödinger equation with a singular, fractional-power potential, referred to as the second Exton potential, are derived and... 
integrable potentials | Stationary Schrödinger equation | energy spectrum | biconfluent Heun equation | Hermite function | EXACTLY SOLUBLE CLASS | QUANTUM | ASTRONOMY & ASTROPHYSICS | Stationary Schrodinger equation | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 07/2019, Volume 127, pp. 89 - 120
In this paper, we prove that the spectral curve Γn of the generalized Lamé equation with the Treibich–Verdier... 
Spectral curve | Degree of the addition map | Generalized Lamé equation | SYSTEM | MATHEMATICS, APPLIED | Generalized Lame equation | PROPERTY | COVERS | MEAN-FIELD EQUATIONS | POTENTIALS | MATHEMATICS | PAINLEVE VI EQUATION | HEUN EQUATION | ANSATZ
Journal Article
Journal of Sound and Vibration, ISSN 0022-460X, 03/2020, Volume 469, p. 115169
This paper aims at presenting closed-form general analytical solutions of the Webster equation describing plane elastic or acoustic waves. The considered... 
Horn | Webster equation | Triconfluent Heun equation | Triconfluent Heun function | Non-uniform cross-sectioned waveguide | ACOUSTICS | MECHANICS | FREE LONGITUDINAL VIBRATION | HORN EQUATION | RODS | ENGINEERING, MECHANICAL | Nonlinear equations | Ducts | Resonant frequencies | Approximations | Exact solutions | Acoustics | Mathematical functions | Polynomials | Acoustic waves
Journal Article
Chemical Physics Letters, ISSN 0009-2614, 05/2017, Volume 676, pp. 169 - 173
[Display omitted] •We construct a double-well potential for which the Schrödinger equation can be exactly solved.•The wave function is expressed via the... 
Confluent Heun’s function | Schrödinger equation | Hydrogen bond | Confluent Heun's function | CHEMISTRY, PHYSICAL | Schrodinger equation | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MOLECULES | Hydrogen | Hydrogen bonding | Bonds | Analysis
Journal Article
Nelineinaya Dinamika, ISSN 1816-448X, 2019, Volume 15, Issue 1, pp. 79 - 85
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2018, Volume 59, Issue 2, p. 22105
We present a definition of integrability for the one-dimensional Schrödinger equation, which encompasses all known integrable systems, i.e., systems for which... 
PHYSICS, MATHEMATICAL | HEUN | Mathematical Physics | Mathematics
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2009, Volume 263, Issue 1, pp. 149 - 194
Several results including integral representation of solutions and Hermite-Krichever Ansatz on Heun's equation are generalized to a certain class of Fuchsian... 
SYSTEM | MATHEMATICS | SCHLESINGER EQUATIONS | COVERS | HEUN EQUATION
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 624 - 630
We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these... 
Confluent hypergeometric function | Bessel function | Confluent Heun equation | Recurrence relation | 02.30.Gp Special functions | 02.30.Hq Ordinary differential equations | 02.30.Mv Approximations and expansions | MATHEMATICS, APPLIED | TERMS
Journal Article
Classical and Quantum Gravity, ISSN 0264-9381, 02/2014, Volume 31, Issue 4, p. 45003
Journal Article
International Journal of Theoretical Physics, ISSN 0020-7748, 3/2018, Volume 57, Issue 3, pp. 652 - 663
For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming... 
Quantum cosmology | Heun functions | Theoretical, Mathematical and Computational Physics | Quantum Physics | Friedmann equation | Physics, general | Physics | Elementary Particles, Quantum Field Theory | COSMOLOGY | SCALAR FIELD | PHYSICS, MULTIDISCIPLINARY | Toiletries industry | Radiation
Journal Article
Constructive Approximation, ISSN 0176-4276, 2014, Volume 39, Issue 1, pp. 75 - 83
Painleve equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas... 
Heun deformed equation | Apparent singularity | Painlevé equation | 2×2 Fuchsian linear system | Heun equation | Euler integral transform | Antiquantization
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2019, Volume 132, pp. 251 - 272
In this paper, the second in a series, we continue to study the generalized Lamé equation with the Treibich-Verdier... 
Mean field equation | Generalized Lamé equation | Pre-modular form | MATHEMATICS | MATHEMATICS, APPLIED | Generalized Lame equation | MEAN-FIELD EQUATIONS | POTENTIALS | HEUN EQUATION
Journal Article
Classical and Quantum Gravity, ISSN 0264-9381, 10/2016, Volume 33, Issue 22, p. 225011
Journal Article
Theoretical and Mathematical Physics(Russian Federation), ISSN 0040-5779, 04/2018, Volume 195, Issue 1, pp. 494 - 512
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2018, Volume 14
We describe the close connection between the linear system for the sixth Painleve equation and the general Heun equation, formulate the Riemann-Hilbert problem... 
Heun polynomials | Painlevé equations | Riemann-Hilbert problem | Painleve equations | MONODROMY | TRANSCENDENTS | PHYSICS, MATHEMATICAL | PAINLEVE | DEFORMATION | ORDINARY DIFFERENTIAL-EQUATIONS | Mathematical analysis
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 07/2018, Volume 14
The q-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these... 
Degeneration | Quasi-Exact solvability | Regular singularity | Heun equation | Q-Deformation | MODELS | regular singularity | quasi-exact solvability | DIFFERENCE-OPERATORS | PHYSICS, MATHEMATICAL | q-deformation | degeneration | Singularities | Subspaces | Deformation
Journal Article
Modern Physics Letters A, ISSN 0217-7323, 05/2018, Volume 33, Issue 16, p. 1850090
We study the wave equation governing massless fields of all spins (s = 0, 1 2 , 1, 3 2 and 2) in the most general spherical symmetric metric of conformal... 
Wave equation | conformal gravity | Heun equation | PERTURBATIONS | QUASI-NORMAL MODES | STABILITY | FIELD | PHYSICS, NUCLEAR | HARMONICS | PHYSICS, MATHEMATICAL | BLACK-HOLES | ASTRONOMY & ASTROPHYSICS | KERR-DE-SITTER | PHYSICS, PARTICLES & FIELDS
Journal Article
by Jiang, M and Wang, XJ and Li, ZH
ASTROPHYSICS AND SPACE SCIENCE, ISSN 0004-640X, 06/2015, Volume 357, Issue 2, pp. 1 - 5
The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We... 
Spin fields | BACKGROUNDS | Heun's equation | PERTURBATIONS | GENERAL-RELATIVITY | Black holes | STABILITY | ASTRONOMY & ASTROPHYSICS | HARMONICS | KERR-DE-SITTER | BLACK-HOLES | Electromagnetism | Studies | Cosmology | Astrophysics | Cosmological constant | Gravitation | Propagation | Mathematical analysis | Neutrinos | Scalars | Black holes (astronomy) | Event horizon
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 09/2016, Volume 106, Issue 3, pp. 546 - 581
In literature, it is known that any solution of Painlevé VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on CP1. In... 
Isomonodromy theory | Hamiltonian system | The elliptic form | Painlevé VI equation | MATHEMATICS | MONODROMY | MATHEMATICS, APPLIED | 2ND-ORDER | Painleve VI equation | DIFFERENTIAL-EQUATIONS | HEUN EQUATION | DEFORMATION
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 5/2014, Volume 179, Issue 2, pp. 543 - 549
Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or... 
apparent singularity | confluent Heun equation | Theoretical, Mathematical and Computational Physics | monodromy | Applications of Mathematics | Physics | Euler integral transform | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL
Journal Article
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