University of Toronto's Symplectic Geometry Seminar

Nov. 24, 2003, 2:10-3

Boris Khesin


"Hamiltonian dynamics on pseudo-differential symbols"


We describe a natural Poisson-Lie group structure on the spaces of pseudo-differential symbols of any complex (or real) order in several variables. In one variable, the corresponding structure generalizes the Adler-Gelfand-Dickey brackets. A universal Hamiltonian dynamical system on the group interpolates between the KP, n-KdV, and NLS flows. In the case of several variables developed recently, the corresponding Hamiltonian system yields a generalization of Parshin's multicomponent KP hierarchy.