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TMF, 2009, Volume 159, Number 1, Pages 64–80 (Mi tmf6333)  

This article is cited in 8 scientific papers (total in 8 papers)

Aspects of proper differential sequences of ordinary differential equations

N. Eulera, P. G. L. Leachb

a Luleå University of Technology
b School of Mathematical Sciences, University of KwaZulu-Natal

Abstract: We define a proper differential sequence of ordinary differential equations and introduce a method for deriving an alternate sequence of integrals for such a sequence. We describe some general properties, illustrated by several examples.

Keywords: sequence of ordinary differential equations, recursion operator, symmetry analysis of ordinary differential equations, integrable ordinary differential equation

DOI: https://doi.org/10.4213/tmf6333

Full text: PDF file (418 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 159:1, 474–487

Bibliographic databases:

Received: 22.05.2008
Revised: 28.08.2008

Citation: N. Euler, P. G. L. Leach, “Aspects of proper differential sequences of ordinary differential equations”, TMF, 159:1 (2009), 64–80; Theoret. and Math. Phys., 159:1 (2009), 474–487

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v159/i1/p64

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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. M. C. Nucci, “Seeking (and finding) Lagrangians”, Theoret. and Math. Phys., 160:1 (2009), 1014–1021  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Leach P.G.L., Euler N., “A novel Riccati sequence”, J. Nonlinear Math. Phys., 16, Suppl. 1 (2009), 157–164  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Pradeep R.G., Chandrasekar V.K., Senthilvelan M., Lakshmanan M., “A nonlocal connection between certain linear and nonlinear ordinary differential equations: extension to coupled equations”, J. Math. Phys., 51:10 (2010), 103513, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. Andriopoulos K., Leach P.G.L., Maharaj A., “On Differential Sequences”, Applied Mathematics & Information Sciences, 5:3 (2011), 525–546  mathscinet  isi
    5. Bruzon M.S., Gandarias M.L., Senthilvelan M., “Nonlocal symmetries of Riccati and Abel chains and their similarity reductions”, J Math Phys, 53:2 (2012), 023512  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Leach P.G.L., “Derivatives of Differential Sequences”, J. Eng. Math., 82:1, SI (2013), 5–16  crossref  mathscinet  zmath  isi  scopus  scopus
    7. M. C. Nucci, “Ubiquitous symmetries”, Theoret. and Math. Phys., 188:3 (2016), 1361–1370  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Charalambous K., Leach P.G.L., Sinuvasan R., “Some Properties of the Nesterenko Differential Sequence”, Quaest. Math., 42:4 (2019), 517–532  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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