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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 2, Pages 304–320
DOI: https://doi.org/10.4213/tmf6089 (Mi tmf6089) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Cylindrical Kadomtsev–Petviashvili equation: Old and new results

C. Kleina, V. B. Matveevb, A. O. Smirnovc

a Max Planck Institute for the Physics of Complex Systems
b Université de Bourgogne
c Saint-Petersburg State University of Aerospace Instrumentation
Full-text PDF (1168 kB) Citations (24)
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DOI: https://doi.org/10.4213/tmf6089
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.
Keywords: Johnson equation, soliton, finite-gap solution, Darboux transformation, lump.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 2, Pages 1132–1145
DOI: https://doi.org/10.1007/s11232-007-0097-x
Bibliographic databases:
Language: Russian
Citation: C. Klein, V. B. Matveev, A. O. Smirnov, “Cylindrical Kadomtsev–Petviashvili equation: Old and new results”, TMF, 152:2 (2007), 304–320; Theoret. and Math. Phys., 152:2 (2007), 1132–1145
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6089
  • https://www.mathnet.ru/eng/tmf/v152/i2/p304
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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