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.

References in corpus (2)

• Remarks on KdV-type Flows on Star-Shaped Curves
• Hamiltonian flows on null curves

Cited by in corpus (6)

• Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
• Integrable Flows for Starlike Curves in Centroaffine Space
• Liouville Correspondences between Integrable Hierarchies
• mKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere
• Toda lattice hierarchy and Goldstein-Petrich flows for plane curves
• On the geometry of star-shaped curves in ${\mathbb{R}}^n$