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Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach

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An Erratum to this article was published on 01 August 2007

Abstract

Functional representations of (matrix) Burgers and potential Kadomtsev-Petviashvili (pKP) hierarchies (and others), as well as some corresponding Bäcklund transformations, can be obtained surprisingly simply from a “discrete” functional zero-curvature equation. We use these representations to show that any solution of a Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy. In particular, this leads to an extension of the Cole-Hopf transformation to the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions of certain functional Riccati equations.

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Authors and Affiliations

  1. Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., GR-82100, Chios, Greece

    A. Dimakis

  2. Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstrasse 10, D-37073, Göttingen, Germany

    F. Müller-Hoissen

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  1. A. Dimakis
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  2. F. Müller-Hoissen
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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 66–82, July, 2007.

An erratum to this article is available at http://dx.doi.org/10.1007/s11232-007-0106-0.

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Dimakis, A., Müller-Hoissen, F. Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach. Theor Math Phys 152, 933–947 (2007). https://doi.org/10.1007/s11232-007-0079-z

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