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 TMF, 2000, Volume 122, Number 1, Pages 58–71 (Mi tmf555)

Existence of a global solution of the Whitham equations

T. Grava

International School for Advanced Studies (SISSA)

Abstract: The Cauchy problem for Whitham equations with monotonic analytic initial data is studied. If the initial data $f(u)$ satisfies the condition $f^{(2N+1)}(u)<0$ for all $u\in\mathbf R$ except a number of isolated points, then the genus of the solution of the Whitham equations is at most equal to $N$, where $1\leq N\in\mathbf N$.

DOI: https://doi.org/10.4213/tmf555

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English version:
Theoretical and Mathematical Physics, 2000, 122:1, 46–57

Bibliographic databases:

Citation: T. Grava, “Existence of a global solution of the Whitham equations”, TMF, 122:1 (2000), 58–71; Theoret. and Math. Phys., 122:1 (2000), 46–57

Citation in format AMSBIB
\Bibitem{Gra00}
\by T.~Grava
\paper Existence of a global solution of the Whitham equations
\jour TMF
\yr 2000
\vol 122
\issue 1
\pages 58--71
\mathnet{http://mi.mathnet.ru/tmf555}
\crossref{https://doi.org/10.4213/tmf555}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1776507}
\zmath{https://zbmath.org/?q=an:0997.37053}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 1
\pages 46--57
\crossref{https://doi.org/10.1007/BF02551169}

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This publication is cited in the following articles:
1. Barkovskii, LM, “Factorization of integro-differential equations of optics of dispersive anisotropic media and tensor integral operators of wave packet velocities”, Optics and Spectroscopy, 90:4 (2001), 561
2. Barkovsky L., Furs A., “Factorization of the one-dimensional wave equations for dispersive media”, Optics of Crystals, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 4358, 2001, 142–147
3. 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
4. Grava, T, “The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit”, Communications on Pure and Applied Mathematics, 55:12 (2002), 1569
5. Barkovsky, LA, “Factorization of integro-differential equations of the acoustics of dispersive viscoelastic anisotropic media and the tensor integral operators of wave packet velocities”, Acoustical Physics, 48:2 (2002), 128
6. 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
7. Maltsev, AY, “Whitham systems and deformations”, Journal of Mathematical Physics, 47:7 (2006), 073505
8. Maltsev A.Ya., “The conservation of the Hamiltonian structures in the deformations of the Whitham systems”, J. Phys. A: Math. Theor., 43:6 (2010), 065202
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