Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
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.
- Publication:
-
SIGMA
- Pub Date:
- May 2012
- DOI:
- 10.3842/SIGMA.2012.030
- arXiv:
- arXiv:1205.5329
- Bibcode:
- 2012SIGMA...8..030M
- Keywords:
-
- local motion of curves;
- integrable evolution equations;
- Kaup-Kupershmidt hierarchy;
- geometric variational problems;
- projective differential geometry;
- Mathematics - Differential Geometry;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- SIGMA 8 (2012), 030, 20 pages