A geometric construction of solutions of the strict dKP(Λ0) hierarchy

G. F. Helminck*, V. A. Poberezhny, S. V. Polenkova

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)

    Abstract

    In a previous paper we associated to each invertible constant pseudo difference operator Λ0 of degree one, two integrable hierarchies in the algebra of pseudo difference operators PsΔ the so-called dKP(Λ0) hierarchy and its strict version. We show here first that both hierarchies can be described as the compatibility conditions for a proper linearization. Next we present a geometric framework for the construction of solutions of the hierarchies, i.e. we associate to each hierarchy an infinite dimensional variety such that to each point of the variety one can construct a solution of the corresponding hierarchy. This yields a Segal–Wilson type framework for all these integrable hierarchies.

    Original languageEnglish
    Pages (from-to)189-203
    Number of pages15
    JournalJournal of geometry and physics
    Volume131
    DOIs
    Publication statusPublished - Sep 2018

    Keywords

    • Compatible Lax equations
    • Flag varieties
    • Linearizations
    • Oscillating and wave matrices
    • Pseudo difference operators
    • Zero curvature form

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