A natural geometric construction underlying a class of Lax pairs

2014/01/03 by Joseph Krasil'shchik, Krasil'shchik, Joseph
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #math.DG #nlin.SI

paper · pdf · doi:10.48550/arxiv.1401.0612

arxiv created 2014/01/03 · arxiv updated 2014/01/06

Abstract

In the framework of the theory of differential coverings \citeKV, we discuss a general geometric construction that serves the base for the so-called Lax pairs containing differentiation with respect to the spectral parameter \citeOS. Such kind of objects arise, for example, when studying integrability properties of equations like the Gibbons-Tsarev one \citeGT.

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