Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system

We consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape o...

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Main Authors:	A. A. Halim, S. P. Kshevetskii, S. B. Leble
Format:	Article
Language:	English
Published:	Hindawi Limited 2003-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/S0161171203212242

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spelling	doaj-1a8407876b4d4d68900d874a7d2c430a2020-11-25T01:06:24ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003633979399310.1155/S0161171203212242Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV systemA. A. Halim0S. P. Kshevetskii1S. B. Leble2Theoretical and Mathematical Physics Department, Gdansk University of Technology, Gdansk 80-952, PolandTheoretical Physics Department, Kaliningrad State University, Kaliningrad 236041, RussiaTheoretical and Mathematical Physics Department, Gdansk University of Technology, Gdansk 80-952, PolandWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is numerically solved via a finite-difference scheme for which we prove the convergence and stability. Together with the solution of the Sturm-Liouville problem, the stream functions give the internal waves profile.http://dx.doi.org/10.1155/S0161171203212242
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A. A. Halim S. P. Kshevetskii S. B. Leble
spellingShingle	A. A. Halim S. P. Kshevetskii S. B. Leble Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system International Journal of Mathematics and Mathematical Sciences
author_facet	A. A. Halim S. P. Kshevetskii S. B. Leble
author_sort	A. A. Halim
title	Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
title_short	Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
title_full	Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
title_fullStr	Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
title_full_unstemmed	Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
title_sort	approximate solution for euler equations of stratified water via numerical solution of coupled kdv system
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2003-01-01
description	We consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is numerically solved via a finite-difference scheme for which we prove the convergence and stability. Together with the solution of the Sturm-Liouville problem, the stream functions give the internal waves profile.
url	http://dx.doi.org/10.1155/S0161171203212242
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system

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