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Symmetry, Integrability and Geometry: Methods and Applications, 2005, Volume 1, 005, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2005.005
(Mi sigma5)
 

This article is cited in 24 scientific papers (total in 24 papers)

Andrew Lenard: A Mystery Unraveled

Jeffery Praught, Roman G. Smirnov

Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5
References:
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.
Received: September 29, 2005; in final form October 3, 2005; Published online October 8, 2005
Bibliographic databases:
Document Type: Article
Language: English
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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  • https://www.mathnet.ru/eng/sigma5
  • https://www.mathnet.ru/eng/sigma/v1/p5
  • This publication is cited in the following 24 articles:
    1. Roman G. Smirnov, Kunpeng Wang, “The Cobb–Douglas Production Function and the Old Bowley's Law”, SIGMA, 20 (2024), 045, 20 pp.  mathnet  crossref
    2. José Luis Jaramillo, Michele Lenzi, Carlos F. Sopuerta, “Integrability in perturbed black holes: Background hidden structures”, Phys. Rev. D, 110:10 (2024)  crossref
    3. Michele Lenzi, Carlos F. Sopuerta, “Black hole greybody factors from Korteweg–de Vries integrals: Theory”, Phys. Rev. D, 107:4 (2023)  crossref
    4. Tempesta P. Tondo G., “Haantjes Algebras of Classical Integrable Systems”, Ann. Mat. Pura Appl., 201:1 (2022), 57–90  crossref  mathscinet  isi
    5. Alexander G. Rasin, Jeremy Schiff, “Four Symmetries of the KdV Equation”, J Nonlinear Sci, 32:5 (2022)  crossref
    6. Hassan Boualem, Robert Brouzet, “Generically, Arnold–Liouville Systems Cannot be Bi-Hamiltonian”, SIGMA, 17 (2021), 096, 17 pp.  mathnet  crossref
    7. Lenzi M., Sopuerta C.F., “Darboux Covariance: a Hidden Symmetry of Perturbed Schwarzschild Black Holes”, Phys. Rev. D, 104:12 (2021), 124068  crossref  mathscinet  isi
    8. A. V. Domrin, B. I. Suleimanov, M. A. Shumkin, “Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies”, Proc. Steklov Inst. Math., 311 (2020), 98–113  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Levandovskiy S.A., Rozhkov G.K., Moller A.B., Tulupov O.N., “The Concept of a Mini-Mill Rerolling Used Rails as a Raw Material”, CIS Iron Steel Rev., 19 (2020), 27–32  crossref  isi  scopus
    10. Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi, Marco Pedroni, “On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations”, SIGMA, 15 (2019), 087, 17 pp.  mathnet  crossref
    11. Olver P.J., “Emmy Noether'S Enduring Legacy in Symmetry”, Symmetry, 29:4 (2018), 475–485  crossref  isi
    12. 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
    13. 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
    14. 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
    15. 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
    16. Adrian Constantin, Boris Kolev, Number Theory, Analysis and Geometry, 2012, 143  crossref
    17. 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
    18. Wang, JP, “Lenard scheme for two-dimensional periodic Volterra chain”, Journal of Mathematical Physics, 50:2 (2009), 023506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. 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
    20. Zhou R., “Mixed hierarchy of soliton equations”, Journal of Mathematical Physics, 50:12 (2009), 123502  crossref  mathscinet  zmath  adsnasa  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Symmetry, Integrability and Geometry: Methods and Applications
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