Cylindrical KP revisited
Christian Klein, Vladimir Matveev, and Alexander Smirnov
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Submission date: 15. Nov. 2006 (revised version: January 2007)
published in: Theoretical and mathematical physics, 152 (2007) 2, p. 1132-1145
DOI number (of the published article): 10.1007/s11232-007-0097-x
with the following different title: Cylindrical Kadomtsev-Petviashvili equation : old and new results
MSC-Numbers: 250xx, 58Hx, 35Qxx
Keywords and phrases: Johnson equation, solitons, finite-gap solutions, Darboux transformations
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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.