Bi-Hamiltonian Structure of a Third-Order Nonlinear Evolution Equation on Plane Curve Motions

摘要

＜正＞ In the present paper,we identify the integrability of the third-order nonlinear evolution equation ut=（1/2）((uxx+u)-2)x in a Hamiltonian viewpoint.We prove that the recursion operator obtained by S.Yu.Sakovich ishereditary,and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditaryoperator.A hierarchy associated to the equation is also shown.