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TMF, 1991, Volume 87, Number 1, Pages 40–47 (Mi tmf5467)  

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

Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations

V. R. Kudashev, S. E. Sharapov


Abstract: Explicit expressions that demonstrate the inheritance of some symmetries of the KdV equations by the Whitham equations for cnoidal KdV waves are obtained. A class of symmetries of Whitham equations of special form is found and described. Explicit expressions that describe a series of self-similar solutions of Whitham equations are obtained.

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English version:
Theoretical and Mathematical Physics, 1991, 87:1, 358–363

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Received: 03.09.1990

Citation: V. R. Kudashev, S. E. Sharapov, “Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations”, TMF, 87:1 (1991), 40–47; Theoret. and Math. Phys., 87:1 (1991), 358–363

Citation in format AMSBIB
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\by V.~R.~Kudashev, S.~E.~Sharapov
\paper Inheritance of~KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations
\jour TMF
\yr 1991
\vol 87
\issue 1
\pages 40--47
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1122778}
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\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 87
\issue 1
\pages 358--363
\crossref{https://doi.org/10.1007/BF01016574}
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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. S. I. Svinolupov, V. V. Sokolov, “Factorization of evolution equations”, Russian Math. Surveys, 47:3 (1992), 127–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. N. G. Mazur, “Quasiclassical asymptotics of the inverse scattering solutions of the KdV equation and the solution of Whitham's modulation equations”, Theoret. and Math. Phys., 106:1 (1996), 35–49  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. El, GA, “Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem”, Physics Letters A, 222:6 (1996), 393  crossref  mathscinet  zmath  adsnasa  isi
    4. Grava T., “From the Solution of the Tsarev System to the Solution of the Whitham Equations”, Math. Phys. Anal. Geom., 4:1 (2001), 65–96  crossref  isi
    5. Grava, T, “Riemann–Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler-Poisson-Darboux type”, Communications on Pure and Applied Mathematics, 55:4 (2002), 395  crossref  mathscinet  zmath  isi
    6. Grava, T, “Whitham equations, Bergman kernel and Lax-Levermore minimizer”, Acta Applicandae Mathematicae, 82:1 (2004), 1  crossref  mathscinet  zmath  isi
    7. Lorenzoni, P, “Flat bidifferential ideals and semi-Hamiltonian PDEs”, Journal of Physics A-Mathematical and General, 39:44 (2006), 13701  crossref  mathscinet  zmath  adsnasa  isi
    8. B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations”, Theoret. and Math. Phys., 168:1 (2011), 963–973  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    9. Konopelchenko B.G. Ortenzi G., “Quasi-Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter”, Stud. Appl. Math., 130:2 (2013), 167–199  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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