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TMF, 2007, Volume 151, Number 3, Pages 486–494 (Mi tmf6061)  

This article is cited in 9 scientific papers (total in 9 papers)

Differential equations uniquely determined by algebras of point symmetries

G. Mannoa, F. Oliverib, R. Vitoloa

a Lecce University
b University of Messina

Abstract: We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some relevant algebras of vector fields on $\mathbb{R}^k$ (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted by the considered Lie algebras.

Keywords: Lie symmetries of differential equations, jet space

DOI: https://doi.org/10.4213/tmf6061

Full text: PDF file (409 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 151:3, 843–850

Bibliographic databases:


Citation: G. Manno, F. Oliveri, R. Vitolo, “Differential equations uniquely determined by algebras of point symmetries”, TMF, 151:3 (2007), 486–494; Theoret. and Math. Phys., 151:3 (2007), 843–850

Citation in format AMSBIB
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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. Andriopoulos K., Dimas S., Leach P.G.L., Tsoubelis D., “On the systematic approach to the classification of differential equations by group theoretical methods”, J. Comput. Appl. Math., 230:1 (2009), 224–232  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Myeni S.M., Leach P.G.L., “Complete symmetry group and nonlocal symmetries for some two-dimensional evolution equations”, J. Math. Anal. Appl., 357:1 (2009), 225–231  crossref  mathscinet  zmath  isi  scopus
    3. Dimas S., Andriopoulos K., Tsoubelis D., Leach P.G.L., “Complete specification of some partial differential equations that arise in financial mathematics”, Journal of Nonlinear Mathematical Physics, 16, Suppl. 1 (2009), 73–92  crossref  zmath  adsnasa  isi  scopus
    4. White H., “Nonlocal symmetries and complete symmetry groups of dynamical systems admitting linearizations”, Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics in Physics, 125:11 (2010), 1363–1378  mathscinet  isi
    5. De Matteis G., Manno G., “Lie Algebra Symmetry Analysis of the Helfrich and Willmore Surface Shape Equations”, Commun. Pure Appl. Anal, 13:1 (2014), 453–481  crossref  mathscinet  zmath  isi  scopus
    6. Manno G., Oliveri F., Saccomandi G., Vitolo R., “Ordinary Differential Equations Described By Their Lie Symmetry Algebra”, J. Geom. Phys., 85 (2014), 2–15  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Pucci E., Saccomandi G., Vitolo R., “Bogus Transformations in Mechanics of Continua”, Int. J. Eng. Sci., 99 (2016), 13–21  crossref  mathscinet  isi  scopus
    8. Sergyeyev A., Vitolo R., “Symmetries and conservation laws for the Karczewska–Rozmej–Rutkowski–Infeld equation”, Nonlinear Anal.-Real World Appl., 32 (2016), 1–9  crossref  mathscinet  zmath  isi  elib  scopus
    9. Gorgone M., Oliveri F., “Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives”, J. Geom. Phys., 113 (2017), 53–64  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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