Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined b...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148468 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarch / E. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862670871019126784 |
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| author | Musso, E. |
| author_facet | Musso, E. |
| citation_txt | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarch / E. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave cnoidal solutions of the fifth-order Kaup-Kupershmidt equation are described.
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| first_indexed | 2025-12-07T15:32:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148468 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:32:21Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Musso, E. 2019-02-18T13:26:26Z 2019-02-18T13:26:26Z 2012 Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarch / E. Musso // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A20; 53A55; 33E05; 35Q53; 37K10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.030 https://nasplib.isofts.kiev.ua/handle/123456789/148468 The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave cnoidal solutions of the fifth-order Kaup-Kupershmidt equation are described. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
 The work was partially supported by MIUR project: Metriche riemanniane e variet`a differenziabili; by the GNSAGA of INDAM and by TTPU University in Tashkent. The author would like to thank the referees and G. Mar´ı Bef fa for their useful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy Article published earlier |
| spellingShingle | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy Musso, E. |
| title | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy |
| title_full | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy |
| title_fullStr | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy |
| title_full_unstemmed | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy |
| title_short | Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy |
| title_sort | motions of curves in the projective plane inducing the kaup-kupershmidt hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148468 |
| work_keys_str_mv | AT mussoe motionsofcurvesintheprojectiveplaneinducingthekaupkupershmidthierarchy |