Multi-Hamiltonian Structures on Spaces of Closed Equicentroaffine Plane Curves Associated to Higher KdV Flows

Abstract

Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces. Multi-Hamiltonian systems describing higher mKdV flows are also given on spaces of closed Euclidean plane curves via the geometric Miura transformation.

References in corpus (6)

• Remarks on KdV-type Flows on Star-Shaped Curves
• Integrable generalizations of Schrodinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces
• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons
• Symplectically-invariant soliton equations from non-stretching geometric curve flows
• Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems

Cited by in corpus (2)

• On the geometry of star-shaped curves in ${\mathbb{R}}^n$
• On centro-affine curves and Backlund transformations of the KdV equation