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Theoretical and Mathematical Physics

, Volume 152, Issue 2, pp 1132–1145 | Cite as

Cylindrical Kadomtsev-Petviashvili equation: Old and new results

  • C. KleinEmail author
  • V. B. Matveev
  • A. O. Smirnov
Article

Abstract

We review results on the cylindrical Kadomtsev-Petviashvili (CKP) equation, also known as the Johnson equation. The presentation is based on our results. In particular, we show that the Lax pairs corresponding to the KP and the CKP equations are gauge equivalent. We also describe some important classes of solutions obtained using the Darboux transformation approach. We present plots of exact solutions of the CKP equation including finite-gap solutions.

Keywords

Johnson equation soliton finite-gap solution Darboux transformation lump 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in SciencesLeipzigGermany
  2. 2.Institut de Mathématique de BourgogneDijonFrance
  3. 3.St. Petersburg University of Aerospace InstrumentationSt. PetersburgRussia

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