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.