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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 2, Pages 233–246
DOI: https://doi.org/10.4213/tmf393 (Mi tmf393) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Integrable Quasilinear Equations

R. Hernandez Heredero

Universidad Complutense, Departamento de Fisica Teorica II
Full-text PDF (233 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf393
Abstract: We develop a classification scheme for integrable third-order scalar evolution equations using the symmetry approach to integrability. We use this scheme to study quasilinear equations of a particular type and prove that several equations that were suspected to be integrable can be reduced to the well-known Korteweg–de Vries and Krichever–Novikov equations via a Miura-type differential substitution.
Keywords: classification of integrable differential equations, formal symmetry approach, differential substitutions.
English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 2, Pages 1516–1528
DOI: https://doi.org/10.1023/A:1021146827078
Bibliographic databases:
Language: Russian
Citation: R. Hernandez Heredero, “Integrable Quasilinear Equations”, TMF, 133:2 (2002), 233–246; Theoret. and Math. Phys., 133:2 (2002), 1516–1528
Citation in format AMSBIB
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\paper Integrable Quasilinear Equations
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 2
\pages 1516--1528
\crossref{https://doi.org/10.1023/A:1021146827078}
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Linking options:
  • https://www.mathnet.ru/eng/tmf393
  • https://doi.org/10.4213/tmf393
  • https://www.mathnet.ru/eng/tmf/v133/i2/p233
    • This publication is cited in the following 3 articles:
    1. Hernandez Heredero R., Euler M., Euler N., Reyes E.G., “Compacton Equations and Integrability: the Rosenau-Hyman and Cooper-Shepard-Sodano Equations”, Discret. Contin. Dyn. Syst., 40:1 (2020), 529–548  crossref  mathscinet  isi  scopus
    2. Hernandez Heredero R. Reyes E.G., “Nonlocal Symmetries, Compacton Equations, and Integrability”, Int. J. Geom. Methods Mod. Phys., 10:9 (2013), 1350046  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Heredero, RH, “Classification of fully nonlinear integrable evolution equations of third order”, Journal of Nonlinear Mathematical Physics, 12:4 (2005), 567  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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:482
    Full-text PDF :208
    References:60
    First page:1
     
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