Step Soliton Generalized Solutions of the Shallow Water Equations
Generalized solutions of the shallow water equations are obtained. One studies the particular case of a generalized soliton function passing by a variable bottom. We consider a case of discontinuity in bottom depth. We assume that the surface elevation is given by a step soliton which is defined u...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/910659 |
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| _version_ | 1849406619182432256 |
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| author | A. C. Alvarez A. Meril B. Valiño-Alonso |
| author_facet | A. C. Alvarez A. Meril B. Valiño-Alonso |
| author_sort | A. C. Alvarez |
| collection | DOAJ |
| description | Generalized solutions of the shallow water equations are obtained.
One studies the particular case of a generalized soliton function passing by a variable bottom.
We consider a case of discontinuity in bottom depth. We assume that the surface elevation
is given by a step soliton which is defined using generalized solutions (Colombeau 1993).
Finally, a system of functional equations is obtained where the amplitudes and celerity
of wave are the unknown parameters. Numerical results are presented showing that the
generalized solution produces good results having physical sense. |
| format | Article |
| id | doaj-art-4ca41770d9cd45a9b3ad903079dd9c49 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4ca41770d9cd45a9b3ad903079dd9c492025-08-20T03:36:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/910659910659Step Soliton Generalized Solutions of the Shallow Water EquationsA. C. Alvarez0A. Meril1B. Valiño-Alonso2Department of Fluid Dynamic, IMPA, Dona Castorina 110, Jardín Botànico, 22460-320 Rio de Janeiro, RJ, BrazilLaboratoire AOC, Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe-à-Pitre, GuadeloupeDepartamento de Matemáticas, Facultad de Matemáticas y Computación, Universidad de la Habana, San Lázaro esq. A L, 10400 La Habana, CubaGeneralized solutions of the shallow water equations are obtained. One studies the particular case of a generalized soliton function passing by a variable bottom. We consider a case of discontinuity in bottom depth. We assume that the surface elevation is given by a step soliton which is defined using generalized solutions (Colombeau 1993). Finally, a system of functional equations is obtained where the amplitudes and celerity of wave are the unknown parameters. Numerical results are presented showing that the generalized solution produces good results having physical sense.http://dx.doi.org/10.1155/2012/910659 |
| spellingShingle | A. C. Alvarez A. Meril B. Valiño-Alonso Step Soliton Generalized Solutions of the Shallow Water Equations Journal of Applied Mathematics |
| title | Step Soliton Generalized Solutions of the Shallow Water Equations |
| title_full | Step Soliton Generalized Solutions of the Shallow Water Equations |
| title_fullStr | Step Soliton Generalized Solutions of the Shallow Water Equations |
| title_full_unstemmed | Step Soliton Generalized Solutions of the Shallow Water Equations |
| title_short | Step Soliton Generalized Solutions of the Shallow Water Equations |
| title_sort | step soliton generalized solutions of the shallow water equations |
| url | http://dx.doi.org/10.1155/2012/910659 |
| work_keys_str_mv | AT acalvarez stepsolitongeneralizedsolutionsoftheshallowwaterequations AT ameril stepsolitongeneralizedsolutionsoftheshallowwaterequations AT bvalinoalonso stepsolitongeneralizedsolutionsoftheshallowwaterequations |