On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy

Franco Magri, Marco Pedroni, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We tackle the problem of interpreting the Darboux transformation for the KP hierarchy and its relations with the modified KP hierarchy from a geometric point of view. This is achieved by introducing the concept of a Darboux covering. We construct a Darboux covering of the KP equations and obtain a new hierarchy of equations, which we call the Darboux-KP hierarchy (DKP). We employ the DKP equations to discuss the relationships among the KP equations, the modified KP equations, and the discrete KP equations. Our approach also handles the various reductions of the KP hierarchy. We show that the KP hierarchy is a projection of the DKP, the mKP hierarchy is a DKP restriction to a suitable invariant submanifold, and that the discrete KP equations are obtained as iterations of the DKP ones.

Original languageBritish English
Pages (from-to)305-325
Number of pages21
JournalCommunications in Mathematical Physics
Volume188
Issue number2
DOIs
StatePublished - 1997

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