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

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Teoreticheskaya i Matematicheskaya Fizika, 1991, Volume 87, Number 1, Pages 40–47 (Mi tmf5467)

This article is cited in 26 scientific papers (total in 26 papers)

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

V. R. Kudashev, S. E. Sharapov

Full-text PDF (700 kB) Citations (26)

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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.

Received: 03.09.1990

English version:
Theoretical and Mathematical Physics, 1991, Volume 87, Issue 1, Pages 358–363
DOI: https://doi.org/10.1007/BF01016574

Bibliographic databases:

Language: Russian

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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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf5467

https://www.mathnet.ru/eng/tmf/v87/i1/p40

This publication is cited in the following 26 articles:

A. M. Kamchatnov, “Gurevich–Pitaevskii problem and its development”, Phys. Usp., 64:1 (2021), 48–82
B. I. Suleimanov, A. M. Shavlukov, “Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation”, Ufa Math. J., 13:2 (2021), 99–106
G.A. El, M.A. Hoefer, “Dispersive shock waves and modulation theory”, Physica D: Nonlinear Phenomena, 333 (2016), 11
Y Kodama, B Konopelchenko, W K Schief, “Critical points, Lauricella functions and Whitham-type equations”, J. Phys. A: Math. Theor., 48:22 (2015), 225202
B. G. Konopelchenko, W. K. Schief, “Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations”, Proc. R. Soc. A., 470:2172 (2014), 20140514
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
G.A. El, V.V. Khodorovskii, A.M. Leszczyszyn, “Refraction of dispersive shock waves”, Physica D: Nonlinear Phenomena, 241:18 (2012), 1567
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
B. Konopelchenko, L. Martínez Alonso, E. Medina, “On the singular sector of the Hermitian random matrix model in the large N limit”, Physics Letters A, 375:5 (2011), 867
B Konopelchenko, L Martínez Alonso, E Medina, “Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler–Poisson–Darboux equation”, J. Phys. A: Math. Theor., 43:43 (2010), 434020
R. N. Garifullin, B. I. Suleimanov, “From weak discontinuities to nondissipative shock waves”, J. Exp. Theor. Phys., 110:1 (2010), 133
Lorenzoni, P, “Flat bidifferential ideals and semi-Hamiltonian PDEs”, Journal of Physics A-Mathematical and General, 39:44 (2006), 13701
G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov, “Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System”, Stud Appl Math, 114:4 (2005), 395
Grava, T, “Whitham equations, Bergman kernel and Lax-Levermore minimizer”, Acta Applicandae Mathematicae, 82:1 (2004), 1
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
G. A. El, R. H. J. Grimshaw, “Generation of undular bores in the shelves of slowly-varying solitary waves”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 12:4 (2002), 1015
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
T. Grava, “Bound to the number of oscillatory phases in the solution of the Whitham-KdV equations”, Physics Letters A, 254:5 (1999), 263
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
El, GA, “Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem”, Physics Letters A, 222:6 (1996), 393

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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