Theoretical and Mathematical Physics

, Volume 152, Issue 2, pp 1132–1145

Cylindrical Kadomtsev-Petviashvili equation: Old and new results


    • Max Planck Institute for Mathematics in Sciences
  • V. B. Matveev
    • Institut de Mathématique de Bourgogne
  • A. O. Smirnov
    • St. Petersburg University of Aerospace Instrumentation

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


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.


Johnson equationsolitonfinite-gap solutionDarboux transformationlump
Download to read the full article text

Copyright information

© Springer Science+Business Media, Inc. 2007