Theoretical and Mathematical Physics

, Volume 152, Issue 2, pp 1132–1145

Cylindrical Kadomtsev-Petviashvili equation: Old and new results

Article

DOI: 10.1007/s11232-007-0097-x

Cite this article as:
Klein, C., Matveev, V.B. & Smirnov, A.O. Theor Math Phys (2007) 152: 1132. doi:10.1007/s11232-007-0097-x

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 equationsolitonfinite-gap solutionDarboux transformationlump

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