### Abstract

An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.

Original language | English |
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Pages (from-to) | 512-518 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 521 |

DOIs | |

State | Published - 1 May 2019 |

### Keywords

- Antiquantization
- Apparent singularity
- Confluent Heun equation
- Fuchsian singularity
- Heun equation
- Isomonodromic property
- Painlevé equation
- Painleve equation

### Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

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**Antiquantization as a specific way from the Statistical physics to the Regular physics.** / Slavyanov, Sergey; Stesik, Olga.

Research output: Contribution to journal › Review article › Research › peer-review

TY - JOUR

T1 - Antiquantization as a specific way from the Statistical physics to the Regular physics

AU - Slavyanov, Sergey

AU - Stesik, Olga

PY - 2019/5/1

Y1 - 2019/5/1

N2 - An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.

AB - An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.

KW - Antiquantization

KW - Apparent singularity

KW - Confluent Heun equation

KW - Fuchsian singularity

KW - Heun equation

KW - Isomonodromic property

KW - Painlevé equation

KW - Painleve equation

UR - http://www.scopus.com/inward/record.url?scp=85060906782&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/antiquantization-specific-way-statistical-physics-regular-physics

U2 - 10.1016/j.physa.2019.01.061

DO - 10.1016/j.physa.2019.01.061

M3 - Review article

VL - 521

SP - 512

EP - 518

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -