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Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
Інший ID:
2010 Mathematics Subject Classification: 53A20; 53A55; 33E05; 35Q53; 37K10
DOI: http://dx.doi.org/10.3842/SIGMA.2012.030
DOI: http://dx.doi.org/10.3842/SIGMA.2012.030
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
420
Завантажень:
213
Анотація:
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.
