Theoretical and Mathematical Physics

, Volume 152, Issue 1, pp 933–947

Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach

  • A. Dimakis
  • F. Müller-Hoissen

DOI: 10.1007/s11232-007-0079-z

Cite this article as:
Dimakis, A. & Müller-Hoissen, F. Theor Math Phys (2007) 152: 933. doi:10.1007/s11232-007-0079-z


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.


Burgers hierarchy Cole-Hopf transformation Kadomtsev-Petviashvili hierarchy functional Riccati equation 

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. Dimakis
    • 1
  • F. Müller-Hoissen
    • 2
  1. 1.Department of Financial and Management EngineeringUniversity of the AegeanChiosGreece
  2. 2.Max-Planck-Institut für Dynamik und SelbstorganisationGöttingenGermany

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