  Langer and Perline proved that if x is a solution of the geometric Airy curve
flow on R^n then there exists a parallel normal frame along x(. ,t) for each t
such that the corresponding principal curvatures satisfy the (n-1) component
modified KdV (vmKdV_n). They also constructed higher order curve flows whose
principal curvatures are solutions of the higher order flows in the vmKdV_n
soliton hierarchy. In this paper, we write down a Poisson structure on the
space of curves in R^n parametrized by the arc-length, show that the geometric
Airy curve flow is Hamiltonian, write down a sequence of commuting
Hamiltonians, and construct Backlund transformations and explicit soliton
solutions.
