New Solutions Generating Technique to Generalized Kompaneets Equation and the Corresponding Heun Functions

Perturbations in a draining vortex can be described analytically in terms of confluent Heun functions. In the context of analogue models of gravity in ideal fluids, we investigate analytically the absorption length of waves in a draining bathtub, a rotating black hole analogue, using confluent Heun functions. We compare our analytical results with the corresponding numerical ones, obtaining excellent agreement.

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Klein–Gordon particle near RN black hole, generalized sl(2) algebra and harmonic oscillator energy

International Journal of Modern Physics A ◽

10.1142/s0217751x19501963 ◽

2019 ◽

Vol 34 (31) ◽

pp. 1950196

Author(s):

J. Sadeghi ◽

M. R. Alipour

Keyword(s):

Differential Equation ◽

Information Theory ◽

Black Hole ◽

Energy Spectrum ◽

Harmonic Oscillator ◽

Three Dimensional ◽

The Other ◽

Thermodynamical Properties ◽

Heun Functions ◽

Klein Gordon

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized [Formula: see text] algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of [Formula: see text], which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

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Non-linear integral equations for Heun functions

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500012943 ◽

1969 ◽

Vol 16 (4) ◽

pp. 281-289 ◽

Cited By ~ 4

Author(s):

B. D. Sleeman

Keyword(s):

Integral Equations ◽

Heun Equation ◽

Mathieu Functions ◽

Special Cases ◽

Mathieu’S Equation ◽

Heun Functions ◽

Non Linear ◽

Linear Integral ◽

Image Position ◽

Linear Integral Equations

Some years ago Lambe and Ward (1) and Erdélyi (2) obtained integral equations for Heun polynomials and Heun functions. The integral equations discussed by these authors were of the formFurther, as is well known, the Heun equation includes, among its special cases, Lamé's equation and Mathieu's equation and so (1.1) may be considered a generalisation of the integral equations satisfied by Lamé polynomials and Mathieu functions. However, integral equations of the type (1.1) are not the only ones satisfied by Lamé polynomials; Arscott (3) discussed a class of non- linear integral equations associated with these functions. This paper then is concerned with discussing the existence of non-linear integral equations satisfied by solutions of Heun's equation.

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Self-Adjointness and Conservation Laws of Frobenius Type Equations

Symmetry ◽

10.3390/sym12121987 ◽

2020 ◽

Vol 12 (12) ◽

pp. 1987

Author(s):

Haifeng Wang ◽

Yufeng Zhang

Keyword(s):

Conservation Laws ◽

Burgers Equation ◽

Kdv Equation ◽

The Self ◽

Kp Equation ◽

Commutative Subalgebra ◽

Kompaneets Equation ◽

Dym Equation ◽

Harry Dym Equation

The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

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RELATIVISTIC KOMPANEETS EQUATION

The Ninth Marcel Grossmann Meeting ◽

10.1142/9789812777386_0568 ◽

2002 ◽

pp. 2329-2331

Author(s):

G. LEÓN SOTO ◽

T. ZANNIAS

Keyword(s):

Kompaneets Equation

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Exact solutions of a quartic potential

Modern Physics Letters A ◽

10.1142/s0217732319502080 ◽

2019 ◽

Vol 34 (26) ◽

pp. 1950208 ◽

Cited By ~ 6

Author(s):

Qian Dong ◽

Guo-Hua Sun ◽

M. Avila Aoki ◽

Chang-Yuan Chen ◽

Shi-Hai Dong

Keyword(s):

Exact Solutions ◽

Quantum System ◽

Analytical Solutions ◽

Wave Functions ◽

Negative Potential ◽

Potential Parameter ◽

Real Numbers ◽

Quartic Potential ◽

Heun Functions ◽

Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

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