Scientific articles

Properties of the algebra psd related to integrable hierarchies

G. F. Helminck^a, E. A. Panasenko<sup>b

a</sup> KdV Institute, University of Amsterdam
^b Derzhavin Tambov State University

Abstract: In this paper we discuss and prove various properties of the algebra of pseudo differential operators related to integrable hierarchies in this algebra, in particular the KP hierarchy and its strict version. Some explain the form of the equations involved or give insight in why certain equations in these systems are combined, others lead to additional properties of these systems like a characterization of the eigenfunctions of the linearizations of the mentioned hierarchies, the description of elementary Darboux transformations of both hierarchies and the search for expressions in Fredholm determinants for the constructed eigenfunctions and their duals.

Keywords: pseudo differential operators, the adjoint, constant term, n-KdV hierarchy, KP hierarchy, strict KP hierarchy, Lax equations.

UDC: 517.958+517.98

Received: 24.03.2020

DOI: 10.20310/2686-9667-2020-25-130-183-195