Atsushi Fujioka, Takashi Kurose, “Multi-Hamiltonian Structures on Spaces of Closed Equicentroaffine Plane Curves Associated to Higher KdV Flows”, SIGMA, 2014, Volume 10,048, 11 pp.

This article is cited in 5 papers

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

Atsushi Fujioka^a, Takashi Kurose^b

^a Department of Mathematics, Kansai University, Suita, 564-8680, Japan
^b Department of Mathematical Sciences, Kwansei Gakuin University, Sanda, 669-1337, Japan

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.

Keywords: motions of curves; equicentroaffine curves; KdV hierarchy; multi-Hamiltonian systems.

MSC: 37K25; 35Q53

Received: October 11, 2013; in final form April 16, 2014; Published online April 22, 2014

Language: English

DOI: 10.3842/SIGMA.2014.048