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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 168, Number 1, Pages 49–64
DOI: https://doi.org/10.4213/tmf6663
(Mi tmf6663)
 

This article is cited in 13 scientific papers (total in 13 papers)

Symmetry analysis and exact solutions of some Ostrovsky equations

M. L. Gandarias, M. S. Bruzón

Departamento de Matematicas, Universidad de Cadiz, Cadiz, Spain
References:
Abstract: We apply the classical Lie method and the nonclassical method to a generalized Ostrovsky equation (GOE) and to the integrable Vakhnenko equation (VE), which Vakhnenko and Parkes proved to be equivalent to the reduced Ostrovsky equation. Using a simple nonlinear ordinary differential equation, we find that for some polynomials of velocity, the GOE has abundant exact solutions expressible in terms of Jacobi elliptic functions and consequently has many solutions in the form of periodic waves, solitary waves, compactons, etc. The nonclassical method applied to the associated potential system for the VE yields solutions that arise from neither nonclassical symmetries of the VE nor potential symmetries. Some of these equations have interesting behavior such as “nonlinear superposition”.
Keywords: classical symmetry, exact solution, partial differential equation.
English version:
Theoretical and Mathematical Physics, 2011, Volume 168, Issue 1, Pages 898–911
DOI: https://doi.org/10.1007/s11232-011-0073-3
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. L. Gandarias, M. S. Bruzón, “Symmetry analysis and exact solutions of some Ostrovsky equations”, TMF, 168:1 (2011), 49–64; Theoret. and Math. Phys., 168:1 (2011), 898–911
Citation in format AMSBIB
\Bibitem{GanBru11}
\by M.~L.~Gandarias, M.~S.~Bruz\'on
\paper Symmetry analysis and exact solutions of some Ostrovsky equations
\jour TMF
\yr 2011
\vol 168
\issue 1
\pages 49--64
\mathnet{http://mi.mathnet.ru/tmf6663}
\crossref{https://doi.org/10.4213/tmf6663}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2021731}
\transl
\jour Theoret. and Math. Phys.
\yr 2011
\vol 168
\issue 1
\pages 898--911
\crossref{https://doi.org/10.1007/s11232-011-0073-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79961163722}
Linking options:
  • https://www.mathnet.ru/eng/tmf6663
  • https://doi.org/10.4213/tmf6663
  • https://www.mathnet.ru/eng/tmf/v168/i1/p49
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:599
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    References:44
    First page:12
     
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