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...

Full description

Saved in:
Bibliographic Details
Main Authors: A. C. Alvarez, A. Meril, B. Valiño-Alonso
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/910659
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849406619182432256
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