Geodesic
Cylindrical Kadomtsev--Petviashvili equation: Old and new results
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 304-320

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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 equation, finite-gap solution, lump.
Mots-clés : soliton, Darboux transformation 
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     author = {C. Klein and V. B. Matveev and A. O. Smirnov},
     title = {Cylindrical {Kadomtsev--Petviashvili} equation: {Old} and new results},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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C. Klein; V. B. Matveev; A. O. Smirnov. Cylindrical Kadomtsev--Petviashvili equation: Old and new results. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 304-320. http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a7/