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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 030, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.030 (Mi sigma707) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Motions of curves in the projective plane. Inducing the Kaup–Kupershmidt hierarchy

Emilio Musso

Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
Full-text PDF (737 kB) Citations (12)
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DOI: https://doi.org/10.3842/SIGMA.2012.030
Abstract: 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.
Keywords: local motion of curves, integrable evolution equations, Kaup–Kupershmidt hierarchy, geometric variational problems, projective differential geometry.
Received: February 8, 2012; in final form May 11, 2012; Published online May 24, 2012
Bibliographic databases:
Document Type: Article
MSC: 53A20, 53A55, 33E05, 35Q53, 37K10
Language: English
Citation: Emilio Musso, “Motions of curves in the projective plane. Inducing the Kaup–Kupershmidt hierarchy”, SIGMA, 8 (2012), 030, 20 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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