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Fundam. Prikl. Mat., 2006, Volume 12, Issue 6, Pages 17–32 (Mi fpm1000)  

Eigenfunctions of structures described by the “shallow water” model in a plane

K. A. Volosov

Moscow State University of Railway Communications

Abstract: We propose a new method for solving the “shallow water” equations. We show that from the equations of the “shallow water” model one obtains nonlinear Liouville type equations, Helmholtz equations, etc. This allows one to construct eigenfunctions of various structures that appear in the flow in the two-dimensional case. We obtain exact and asymptotic solutions in an elliptic domain with singularities.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:1, 2639–2650

Bibliographic databases:

Document Type: Article
UDC: 517.9

Citation: K. A. Volosov, “Eigenfunctions of structures described by the “shallow water” model in a plane”, Fundam. Prikl. Mat., 12:6 (2006), 17–32; J. Math. Sci., 151:1 (2008), 2639–2650

Citation in format AMSBIB
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\by K.~A.~Volosov
\paper Eigenfunctions of structures described by the ``shallow water'' model in a~plane
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 6
\pages 17--32
\mathnet{http://mi.mathnet.ru/fpm1000}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314129}
\zmath{https://zbmath.org/?q=an:1151.76396}
\elib{http://elibrary.ru/item.asp?id=11143805}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 1
\pages 2639--2650
\crossref{https://doi.org/10.1007/s10948-008-0162-1}
\elib{http://elibrary.ru/item.asp?id=13592574}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449110924}


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  • Фундаментальная и прикладная математика
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