On algebro-geometric solutions to the Gelfand–Dickey hierarchy

Source abstract

Abstract In [15] Dubrovin introduced an A1-type infinite ODE system and gave a simple way of constructing algebro-geometric solutions to the KdV hierarchy (cf. also [5, 16]). In [39] the infinite ODE system is generalized to g-type infinite ODE system, where g is any simple Lie algebra. In this paper, we give a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy based on the An-type infinite
ODE system and Dubrovin’s method. As an application, we give a formula for the N-point function for the related Riemann θ-function.