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SIGMA, 2005, Volume 1, 005, 7 pages (Mi sigma5)  

This article is cited in 12 scientific papers (total in 12 papers)

Andrew Lenard: A Mystery Unraveled

Jeffery Praught, Roman G. Smirnov

Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5

Abstract: The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the “Lenard recursion formula”. The story about the discovery of the formula told by Andrew Lenard is the subject of this article.

Keywords: Lenard's recursion formula; bi-Hamiltonian formalism; Korteweg–de Vries equation

DOI: https://doi.org/10.3842/SIGMA.2005.005

Full text: PDF file (194 kB)
Full text: http://emis.mi.ras.ru/.../Paper005
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Bibliographic databases:

ArXiv: nlin.SI/0510055
MSC: 01A60; 35Q53; 35Q51; 70H06
Received: September 29, 2005; in final form October 3, 2005; Published online October 8, 2005
Language:

Citation: Jeffery Praught, Roman G. Smirnov, “Andrew Lenard: A Mystery Unraveled”, SIGMA, 1 (2005), 005, 7 pp.

Citation in format AMSBIB
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\by Jeffery Praught, Roman G. Smirnov
\paper Andrew Lenard: A~Mystery Unraveled
\jour SIGMA
\yr 2005
\vol 1
\papernumber 005
\totalpages 7
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\crossref{https://doi.org/10.3842/SIGMA.2005.005}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2173592}
\zmath{https://zbmath.org/?q=an:1128.37045}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kolev, B, “Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 365:1858 (2007), 2333  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Kolev B., “Geometric Differences between the Burgers and the Camassa-Holm Equations”, Journal of Nonlinear Mathematical Physics, 15 (2008), 116–132, Suppl. 2  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Wang, JP, “Lenard scheme for two-dimensional periodic Volterra chain”, Journal of Mathematical Physics, 50:2 (2009), 023506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. A. V. Bolsinov, K. M. Zuev, “A Formal Frobenius Theorem and Argument Shift”, Math. Notes, 86:1 (2009), 10–18  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Zhou R., “Mixed hierarchy of soliton equations”, Journal of Mathematical Physics, 50:12 (2009), 123502  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Rasin A.G., Schiff J., “Infinitely many conservation laws for the discrete KdV equation”, Journal of Physics A-Mathematical and Theoretical, 42:17 (2009), 175205  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Mikhailov A. V., “Introduction”, Lecture Notes in Physics, 767, 2009, 1–15  crossref  mathscinet  zmath  scopus
    8. Baldwin D.E., Hereman W., “A symbolic algorithm for computing recursion operators of nonlinear partial differential equations”, Int J Comput Math, 87:5 (2010), 1094–1119  crossref  mathscinet  zmath  isi  elib  scopus
    9. Tempesta P., Tondo G., “Generalized Lenard Chains, Separation of Variables, and Superintegrability”, Phys. Rev. E, 85:4, 2 (2012), 046602  crossref  mathscinet  adsnasa  isi  elib  scopus
    10. Rasin A.G., Schiff J., “The Gardner Method for Symmetries”, J. Phys. A-Math. Theor., 46:15 (2013), 155202  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Du D., Yang X., “An Alternative Approach To Solve the Mixed AKNS Equations”, J. Math. Anal. Appl., 414:2 (2014), 850–870  crossref  mathscinet  zmath  isi  elib  scopus
    12. Tondo G., “Generalized Lenard Chains and Multi-Separability of the Smorodinsky-Winternitz System”, Physics and Mathematics of Nonlinear Phenomena 2013 (Pmnp2013), Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012042  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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