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Integrable systems in magnetic fields: the generalized parabolic cylindrical case

Author:
O. Kubů, A. Marchesiello, L. Šnobl
Keyword:
Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)
journal:
--
date:
2024-03-08 00:00:00
Abstract
This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to non-subgroup-type coordinates. We find 3 new systems, two with magnetic fields polynomial in Cartesian coordinates and one with unbounded exponential terms. The limit in the parameters of the integrals yields a new parabolic cylindrical system; the limit of vanishing magnetic fields leads to the free motion. This confirms the conjecture that non-subgroup type integrals can be related to separable systems only in a trivial manner.
PDF: Integrable systems in magnetic fields: the generalized parabolic cylindrical case.pdf
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