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

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

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 25 scientific papers (total in 25 papers)

Cylindrical Kadomtsev–Petviashvili equation: Old and new results

C. Klein^a, V. B. Matveev^b, A. O. Smirnov^c

^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 (25)

References:

PDF

HTML

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

\Bibitem{KleMatSmi07}

\by C.~Klein, V.~B.~Matveev, A.~O.~Smirnov

\paper Cylindrical Kadomtsev--Petviashvili equation: Old and new results

\jour TMF

\yr 2007

\vol 152

\issue 2

\pages 304--320

\mathnet{http://mi.mathnet.ru/tmf6089}

\crossref{https://doi.org/10.4213/tmf6089}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2429282}

\zmath{https://zbmath.org/?q=an:1131.35072}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2007TMP...152.1132K}

\elib{https://elibrary.ru/item.asp?id=9541937}

\transl

\jour Theoret. and Math. Phys.

\yr 2007

\vol 152

\issue 2

\pages 1132--1145

\crossref{https://doi.org/10.1007/s11232-007-0097-x}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000249211500009}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548460309}

Linking options:

https://www.mathnet.ru/eng/tmf6089

https://doi.org/10.4213/tmf6089

https://www.mathnet.ru/eng/tmf/v152/i2/p304

This publication is cited in the following 25 articles:

Nazia Batool, W. Masood, Maryam Al Huwayz, Aljawhara H. Almuqrin, Samir A. El-Tantawy, “Interaction of two-dimensional electron-acoustic solitary waves in a cylindrical geometry and their applications in space plasmas”, Physics of Plasmas, 32:4 (2025)
Zhao Zhang, Wencheng Hu, Qi Guo, Yury Stepanyants, “Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:1 (2024)
Xiangyu Yang, Zhen Wang, Zhao Zhang, “Solitons and lump waves to the elliptic cylindrical Kadomtsev–Petviashvili equation”, Communications in Nonlinear Science and Numerical Simulation, 131 (2024), 107837
Wencheng Hu, Zhao Zhang, Qi Guo, Yury Stepanyants, “Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:1 (2024)
Nerijus Sidorovas, Dmitri Tseluiko, Wooyoung Choi, Karima Khusnutdinova, “Nonlinear concentric water waves of moderate amplitude”, Wave Motion, 128 (2024), 103295
L. Ostrovsky, E. Pelinovsky, V. Shrira, Y. Stepanyants, “Localized wave structures: Solitons and beyond”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:6 (2024)
V. B. Matveev, A. O. Smirnov, “Elliptic solitons and «freak waves»”, St. Petersburg Math. J., 33:3 (2022), 523–551
Peng W.-Q., Tian Sh.-F., Zhang T.-T., “Dynamics of the Soliton Waves, Breather Waves, and Rogue Waves to the Cylindrical Kadomtsev-Petviashvili Equation in Pair-Ion-Electron Plasma”, Phys. Fluids, 31:10 (2019), 102107
Gaillard P., “The Johnson Equation, Fredholm and Wronskian Representations of Solutions, and the Case of Order Three”, Adv. Math. Phys., 2018, 1642139
Jahangir R., Masood W., Siddiq M., Batool N., “Interaction and Resonance of Fast Magnetoacoustic Solitary Waves in Cylindrical Geometry For Dense Astrophysical Plasmas”, Phys. Plasmas, 25:10 (2018), 102113
Pierre Gaillard, “Multiparametric families of solutions to the Johnson equation.”, J. Phys.: Conf. Ser., 1141 (2018), 012102
Stjepan Lugomer, “Laser generated Richtmyer–Meshkov and Rayleigh–Taylor instabilities and nonlinear wave-vortex paradigm in turbulent mixing. II. Near-central region of Gaussian spot”, Laser Part. Beams, 35:2 (2017), 210
V. B. Matveev, A. O. Smirnov, “Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach”, Theoret. and Math. Phys., 186:2 (2016), 156–182
Horikis T.P., Frantzeskakis D.J., “Ring Dark and Antidark Solitons in Nonlocal Media”, Opt. Lett., 41:3 (2016), 583–586
Lugomer S., “Laser generated Richtmyer?Meshkov instability and nonlinear wave paradigm in turbulent mixing: I. Central region of Gaussian spot”, Laser Part. Beams, 34:4 (2016), 687–704
Wang M., Zhang J., Li X., “Decay mode solutions to cylindrical KP equation”, Appl. Math. Lett., 62 (2016), 29–34
Batool N., Masood W., Siddiq M., Jahangir R., “Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma”, Phys. Plasmas, 23:8 (2016), 082306
Khusnutdinova K.R., Zhang X., “Long ring waves in a stratified fluid over a shear?flow”, J. Fluid Mech., 794 (2016), 17–44
Lu Zhuo-Sheng, Ren Wen-Xiu, “Wronskian Form Solutions For a Variable Coefficient Kadomtsev-Petviashvili Equation”, Commun. Theor. Phys., 61:3 (2014), 339–343
A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	636
Full-text PDF :	380
References:	70
First page:	5

Registration to the website

Logotypes