On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems
The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149242 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems / M.V. Pavlov, Z. Popowicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Pavlov, M.V. Popowicz, Z. 2019-02-19T19:14:52Z 2019-02-19T19:14:52Z 2009 On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems / M.V. Pavlov, Z. Popowicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 7 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q53 https://nasplib.isofts.kiev.ua/handle/123456789/149242 The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found. This paper is a contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 19–22, 2008, Prague, Czech Republic). We thank Eugeni Ferapontov, Sergey Tsarev and Sergey Zykov for their stimulating and clarifying discussions. M.V.P. would like to thank the Institute of Theoretical Physics of Wroc law University for the hospitality and the Kasa Mianowski Foundation for the financial support of MVP’s visit to Wroc law making this collaboration possible. MVP is grateful to professor Boris Dubrovin for a hospitality in SISSA in Trieste (Italy) where part of this work has been done. MVP was partially supported by the Russian-Italian Research Project (Consortium E.I.N.S.T.E.IN and RFBR grant 06-01-92053). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems |
| spellingShingle |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems Pavlov, M.V. Popowicz, Z. |
| title_short |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems |
| title_full |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems |
| title_fullStr |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems |
| title_full_unstemmed |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems |
| title_sort |
on integrability of a special class of two-component (2+1)-dimensional hydrodynamic-type systems |
| author |
Pavlov, M.V. Popowicz, Z. |
| author_facet |
Pavlov, M.V. Popowicz, Z. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149242 |
| citation_txt |
On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems / M.V. Pavlov, Z. Popowicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 7 назв. — англ. |
| work_keys_str_mv |
AT pavlovmv onintegrabilityofaspecialclassoftwocomponent21dimensionalhydrodynamictypesystems AT popowiczz onintegrabilityofaspecialclassoftwocomponent21dimensionalhydrodynamictypesystems |
| first_indexed |
2025-11-27T17:07:04Z |
| last_indexed |
2025-11-27T17:07:04Z |
| _version_ |
1850852579377938432 |