New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00369544" target="_blank" >RIV/68407700:21240/23:00369544 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/23:00369544

Result on the web

<a href="https://doi.org/10.1140/epjp/s13360-023-04464-6" target="_blank" >https://doi.org/10.1140/epjp/s13360-023-04464-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-023-04464-6" target="_blank" >10.1140/epjp/s13360-023-04464-6</a>

Result language

angličtina

Original language name

New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Original language description

We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike in the case with only scalar potential, quadratic integrability with velocity dependent potentials does not imply separability in the configuration space. The leading order terms in the pairs of commuting integrals can either generalize or have no relation to the forms leading to separation in the absence of a vector potential. We call such pairs of integrals generalized, to distinguish them from the standard ones, which would correspond to separation. Here we focus on three cases of generalized non-subgroup type integrals, namely elliptic cylindrical, prolate/oblate spheroidal and circular parabolic integrals, together with one case not related to any coordinate system. We find two new integrable systems, non-separable in the configuration space, both with generalized elliptic cylindrical integrals. In the other cases, all systems found were already known and possess standard pairs of integrals. In the limit of vanishing vector potential, both systems reduce to free motion and therefore separate in every orthogonal coordinate system.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

EUROPEAN PHYSICAL JOURNAL PLUS

ISSN

2190-5444

e-ISSN

—

Volume of the periodical

138

Issue of the periodical within the volume

9

Country of publishing house

DE - GERMANY

Number of pages

24

Pages from-to

1-24

UT code for WoS article

001075707200010

EID of the result in the Scopus database

2-s2.0-85172394124