|
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.
Full text:
PDF file (165 kB)
References:
PDF file
HTML file
English version:
Journal of Mathematical Sciences (New York), 2008, 151:1, 2639–2650
Bibliographic databases:
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
\Bibitem{Vol06}
\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{https://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{https://elibrary.ru/item.asp?id=13592574}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449110924}
Linking options:
http://mi.mathnet.ru/eng/fpm1000 http://mi.mathnet.ru/eng/fpm/v12/i6/p17
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
|
Number of views: |
This page: | 301 | Full text: | 109 | References: | 21 |
|