Integrable magnetic geodesic flows on 2-surfaces Full article
| Journal |
Nonlinearity
ISSN: 0951-7715 , E-ISSN: 1361-6544 |
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| Output data | Year: 2023, Volume: 36, Number: 4, Pages: 2128-2147 Pages count : 20 DOI: 10.1088/1361-6544/acc0c5 | ||||
| Tags | magnetic geodesic flow, first integral, semi-Hamiltonian system, generalized hodograph method, Riemann invariants, Legendre transformation, hypergeometric functions | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Mathematical Center in Akademgorodok | 075-15-2019-1675 |
Abstract:
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of partial differential equations (PDEs) appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method,inthesecondcaseviatheLegendre transformation and the method of separation of variables.
Cite:
Agapov S.
, Potashnikov A.
, Shubin V.
Integrable magnetic geodesic flows on 2-surfaces
Nonlinearity. 2023. V.36. N4. P.2128-2147. DOI: 10.1088/1361-6544/acc0c5 WOS Scopus РИНЦ OpenAlex
Integrable magnetic geodesic flows on 2-surfaces
Nonlinearity. 2023. V.36. N4. P.2128-2147. DOI: 10.1088/1361-6544/acc0c5 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 12, 2022 |
| Accepted: | Mar 2, 2023 |
| Published print: | Mar 15, 2023 |
| Published online: | Mar 15, 2023 |
Identifiers:
| Web of science: | WOS:000948982900001 |
| Scopus: | 2-s2.0-85150530616 |
| Elibrary: | 61660007 |
| OpenAlex: | W4324382272 |