Ordering of two small parameters in the shallow water wave problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F13%3A%230000371" target="_blank" >RIV/47813059:19610/13:#0000371 - isvavai.cz</a>
Result on the web
<a href="http://iopscience.iop.org/1751-8121/46/7/075501/" target="_blank" >http://iopscience.iop.org/1751-8121/46/7/075501/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/46/7/075501" target="_blank" >10.1088/1751-8113/46/7/075501</a>

Result language
angličtina
Original language name
Ordering of two small parameters in the shallow water wave problem
Original language description
The classical problem of irrotational long waves on the surface of a shallow layer of an ideal fluid moving under the influence of gravity as well as surface tension is considered. A systematic procedure for deriving an equation for surface elevation fora prescribed relation between the orders of the two expansion parameters, the amplitude parameter $alpha$ and the long wavelength (or shallowness) parameter $beta$, is developed. Unlike the heuristic approaches found in the literature, when modifications are made in the equation for surface elevation itself, the procedure starts from the consistently truncated asymptotic expansions for unidirectional waves, a counterpart of the Boussinesq system of equations for the surface elevation and the bottom velocity, from which the leading order and higher order equations for the surface elevation can be obtained by iterations. The relations between the orders of the two small parameters are taken in the form $beta=O(alpha^n)$ and $alpha=O
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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