International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 63, Pages 3979-3993
doi:10.1155/S0161171203212242
Approximate solution for Euler equations of
stratified water via numerical solution of coupled KdV system
1Theoretical and Mathematical Physics Department, Gdansk University of Technology, Gdansk 80-952, Poland
2Theoretical Physics Department, Kaliningrad State University, Kaliningrad 236041, Russia
Received 23 December 2002
Copyright © 2003 A. A. Halim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.