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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 2, Pages 170–183
DOI: https://doi.org/10.4213/tmf388 (Mi tmf388) 		 
This article is cited in 633 scientific papers (total in 633 papers)

A New Integrable Equation with Peakon Solutions

A. Degasperisa, D. D. Holmb, A. Honec

a University of Rome "La Sapienza"
b Los Alamos National Laboratory
c University of Kent
Full-text PDF (293 kB) Citations (633)
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DOI: https://doi.org/10.4213/tmf388
Abstract: We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa–Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to a negative flow in the Kaup–Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa–Holm peakons.
Keywords: peakons, reciprocal transformations, weak solutions.
English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 2, Pages 1463–1474
DOI: https://doi.org/10.1023/A:1021186408422
Bibliographic databases:
Language: Russian
Citation: A. Degasperis, D. D. Holm, A. Hone, “A New Integrable Equation with Peakon Solutions”, TMF, 133:2 (2002), 170–183; Theoret. and Math. Phys., 133:2 (2002), 1463–1474
Citation in format AMSBIB
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\by A.~Degasperis, D.~D.~Holm, A.~Hone
\paper A~New Integrable Equation with Peakon Solutions
\jour TMF
\yr 2002
\vol 133
\issue 2
\pages 170--183
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\crossref{https://doi.org/10.4213/tmf388}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2001531}
\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 2
\pages 1463--1474
\crossref{https://doi.org/10.1023/A:1021186408422}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000180061400004}
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  • https://www.mathnet.ru/eng/tmf/v133/i2/p170
    • This publication is cited in the following 633 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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