MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Cylindrical KP revisited

Christian Klein, Vladimir Matveev and Alexander Smirnov


The aim of this article is to summarize results connected with the cylindrical KP equation (CKP equation) also known as Johnson equation. In particular, we explain the gauge equivalence of the related Lax pairs. We also describe some important classes of explicit solutions obtained by the use of the Darboux transformation approach. Plots of explicit solutions including finite gap solutions to the CKP equation are presented.

MSC Codes:
250xx, 58Hx, 35Qxx
Johnson equation, solitons, finite-gap solutions, Darboux transformations

Related publications

2007 Repository Open Access
Christian Klein, V. B. Matveev and A. O. Smirnov

Cylindrical Kadomtsev-Petviashvili equation : old and new results

In: Theoretical and mathematical physics, 152 (2007) 2, pp. 1132-1145