A New Case of Separability in a Quartic Henon-Heiles System

被引：0

作者：

Sottocornola, Nicola ^{[1
]}

机构：

[1] Zayed Univ, Dept Math & Stat, Abu Dhabi, U Arab Emirates

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2021年 / 28卷 / 03期

关键词：

Integrable systems; separation of coordinates; integration in quadratures;

D O I：

10.2991/jnmp.k.210419.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There are four quartic integrable Henon-Heiles systems. Only one of them has been separated in the generic form while the other three have been solved only for particular values of the constants. We consider two of them, related by a canonical transformation, and we give their separation coordinates in a new case. (C) 2021 The Author. Published by Atlantis Press B.V.

引用

页码：303 / 308

页数：6

共 10 条

[1] INTEGRABLE QUARTIC POTENTIALS AND COUPLED KDV EQUATIONS [J].

BAKER, S ;

ENOLSKII, VZ ;

FORDY, AP .

PHYSICS LETTERS A, 1995, 201 (2-3) :167-174

[2]

Kowalevski S., 1889, Acta Math, V12, P177, DOI [10.1007/BF02592182, DOI 10.1007/BF02592182]

[3] The Kowalevski's top and the method of syzygies [J].

Magri, F .

ANNALES DE L INSTITUT FOURIER, 2005, 55 (06) :2147-2159

[4]

Magri F., 2021, P S PURE MATH

[5]

Magri F., 2018, KOWALEWSKIS TOP REVI

[6] GENERALIZED SEPARABILITY FOR A HAMILTONIAN WITH NONSEPARABLE QUARTIC POTENTIAL [J].

RAVOSON, V ;

RAMANI, A ;

GRAMMATICOS, B .

PHYSICS LETTERS A, 1994, 191 (1-2) :91-95

[7] DIRECT CONSTRUCTION OF A BI-HAMILTONIAN STRUCTURE FOR CUBIC HENON-HEILES SYSTEMS [J].

Sottocornola, Nicola .

JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2020, 57 :99-109

[8] Separation coordinates in Henon-Heiles systems [J].

Sottocornola, Nicola .

PHYSICS LETTERS A, 2019, 383 (36)

[9] Explicit integration of a generic Henon-Heiles system with quartic potential [J].

Sottocornola, Nicola .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2017, 24 (03) :346-355

[10] General solution for Hamiltonians with extended cubic and quartic potentials [J].

Verhoeven, C ;

Musette, M ;

Conte, R .

THEORETICAL AND MATHEMATICAL PHYSICS, 2003, 134 (01) :128-138

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