The Kadomtsev–Petviashvili hierarchy and the Schottky problem

The article is based on a special course delivered by the author in the Independent Moscow university. It contains a detailed explanation of several interrelations between soliton equations, infinite dimensional Grassmann manifold and jacobians of the algebraic curves. All these permit one to prove the (weakened) version of S. P. Novikov's conjecture (based on I. M. Krichever's results) on characterization of jacobians among all abelian tori by cheking whether the (corrected) theta-function of the given abelian variety is a solution of the Kadomtsev–Petviashvili non-linear differential equation.