Algebro-Geometric Solutions of the Gelfand-Dickey Hierarchy (Boussinesq Hierarchy)

The principal subject of this proposal concerns algebro-geometric quasiperiodic solutions of the Gelfand-Dickey hierarchy and certain limiting cases thereof. In addition, in the case of strictly periodic solutions, we intend to derive a variety of new results in Floquet theory of associated n-th order differential expressions $L_n$ with periodic coefficients through a detailed study of the diagonal Green's function $G_n(z,x,x), z \in \cz, x \in \rz$ of $L_n$. Furthermore, trace formulas for first-order self-adjoint Hamiltonian systems will be derived.