The Weyl Algebra, Bispectral Operators and Dynamics of Poles

The present paper reviews some new results in the study of the bispectral problem. We describe all bispectral operators in the Weyl algebra and the Darboux transformations of them. The dynamics of their poles is shown to be connected with the KP-hierarchy. The exposition is intended for readers with some experience in the subject. On the other hand being self-contained it can be used for a first acquaintance with the subject of bispectral operators.