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SIGMA, 2012, Volume 8, 030, 20 pages (Mi sigma707)  

This article is cited in 8 scientific papers (total in 8 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

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.

DOI: https://doi.org/10.3842/SIGMA.2012.030

Full text: PDF file (737 kB)
Full text: http://emis.mi.ras.ru/.../030
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Bibliographic databases:

ArXiv: 1205.5329
MSC: 53A20, 53A55, 33E05, 35Q53, 37K10
Received: February 8, 2012; in final form May 11, 2012; Published online May 24, 2012
Language:

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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\by Emilio Musso
\paper Motions of curves in the projective plane. Inducing the Kaup--Kupershmidt hierarchy
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\vol 8
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Changzheng Qu, Junfeng Song, Ruoxia Yao, “Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries”, SIGMA, 9 (2013), 001, 19 pp.  mathnet  crossref  mathscinet
    2. Annalisa Calini, Thomas Ivey, Gloria Marí-Beffa, “Integrable Flows for Starlike Curves in Centroaffine Space”, SIGMA, 9 (2013), 022, 21 pp.  mathnet  crossref  mathscinet
    3. C. Qu, J. Han, J. Kang, “Backlund transformations for integrable geometric curve flows”, Symmetry-Basel, 7:3 (2015), 1376–1394  crossref  mathscinet  zmath  isi  scopus
    4. C. Qu, Y. Li, “Symplectic invariants for curves and integrable systems in similarity symplectic geometry”, Sci. China-Math., 58:7 (2015), 1415–1432  crossref  mathscinet  zmath  isi  scopus
    5. Jing Kang, Xiaochuan Liu, Peter J. Olver, Changzheng Qu, “Liouville Correspondences between Integrable Hierarchies”, SIGMA, 13 (2017), 035, 26 pp.  mathnet  crossref
    6. J. Song, C. Qu, R. Yao, “Integrable systems and invariant curve flows in symplectic Grassmannian space”, Physica D, 349 (2017), 1–11  crossref  mathscinet  zmath  isi  scopus
    7. Zhou K., Song J., Shen Sh., Ma W.-X., “A Combined Short Pulse-Mkdv Equation and Its Exact Solutions By Two-Dimensional Invariant Subspaces”, Rep. Math. Phys., 83:3 (2019), 339–347  crossref  isi
    8. Horocholyn S.A., “On the Geometry of Star-Shaped Curves in R-N”, Kyushu J. Math., 73:1 (2019), 123–144  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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