, Volume 152, Issue 2, pp 1132-1145

Cylindrical Kadomtsev-Petviashvili equation: Old and new results

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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.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 304–320, August, 2007.