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A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI.

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Title: A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI.
Authors: Marquette, I1 (AUTHOR), Post, S2 (AUTHOR) spost@hawaii.edu, Ritter, L2 (AUTHOR)
Source: Journal of Physics A: Mathematical & Theoretical. 4/16/2022, Vol. 55 Issue 15, p1-17. 17p.
Subjects: Hermite polynomials, Harmonic oscillators, Wave functions, Nonlinear equations, Orthogonal polynomials, Jacobi polynomials
Abstract: We discuss a family of Hamiltonians given by particular rational extensions of the singular oscillator in two-dimensions. The wave functions of these Hamiltonians can be expressed in terms of products of Laguerre and exceptional Jacobi polynomials. We show that these systems are superintegrable and admit an integral of motion that is of fourth-order. As such systems have been classified, we see that these potentials satisfy a non-linear equation related to Painlevé VI. We begin by demonstrating the process with the simpler example of rational extensions of the harmonic oscillator and use the classification of third-order superintegrable systems to connect these families with the known solutions of Painlevé IV associated with Hermite polynomials. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 155867290
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PubType: Academic Journal
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  Data: A family of fourth-order superintegrable systems with rational potentials related to PainlevĂ© VI.
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  Data: <searchLink fieldCode="AR" term="%22Marquette%2C+I%22">Marquette, I</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Post%2C+S%22">Post, S</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> spost@hawaii.edu</i><br /><searchLink fieldCode="AR" term="%22Ritter%2C+L%22">Ritter, L</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 4/16/2022, Vol. 55 Issue 15, p1-17. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Hermite+polynomials%22">Hermite polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Wave+functions%22">Wave functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobi+polynomials%22">Jacobi polynomials</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We discuss a family of Hamiltonians given by particular rational extensions of the singular oscillator in two-dimensions. The wave functions of these Hamiltonians can be expressed in terms of products of Laguerre and exceptional Jacobi polynomials. We show that these systems are superintegrable and admit an integral of motion that is of fourth-order. As such systems have been classified, we see that these potentials satisfy a non-linear equation related to PainlevĂ© VI. We begin by demonstrating the process with the simpler example of rational extensions of the harmonic oscillator and use the classification of third-order superintegrable systems to connect these families with the known solutions of PainlevĂ© IV associated with Hermite polynomials. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1088/1751-8121/ac550a
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Harmonic oscillators
        Type: general
      – SubjectFull: Wave functions
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      – SubjectFull: Nonlinear equations
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      – SubjectFull: Orthogonal polynomials
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      – SubjectFull: Jacobi polynomials
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              M: 04
              Text: 4/16/2022
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