Geometry of the KP hierarchy and string equations.

摘要

n part I, we review the basic results of the KP and Toda lattice theory, Hamiltonian and orthogonal polynomials theories. Also we will give a brief introduction to the constrained KP hierarchy.;In Part II, we use three sections to deal with three different topics. In S1, we show that a family of compatible symplectic structures for an isospectral pseudo-differential operator L (of the KP hierarchy) is obtained by taking the Lie derivative of the first symplectic structure with respect to symmetry Virasoro vector fields