G. F. Helminck, E. A. Panasenko, S. V. Polenkova, “Bilinear equations for the strict KP hierarchy”, TMF, 2015, Volume 185, Number 3,Pages <nobr>512

This article is cited in 3 papers

Bilinear equations for the strict KP hierarchy

G. F. Helminck^a, E. A. Panasenko^b, S. V. Polenkova^c

^a Korteweg—de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands
^b Derzhavin State University, Tambov, Russia
^c University of Twente, Enschede, The Netherlands

Abstract: We describe two modules for the algebra $P\!sd$ of pseudodifferential operators; for each of them, we define an associated system from which the Lax equations of the strict KP hierarchy can be obtained as compatibility conditions. We construct a set of bilinear equations on these modules that characterizes solutions of the strict KP hierarchy that are obtained by dressing the basic generator of $P\!sd$.

Keywords: integrable deformation, pseudodifferential operator, compatible Lax equation, strict KP hierarchy, dual wave function, bilinear form.

DOI: 10.4213/tmf8893