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Mathematical Problems in Engineering
Volume 2015, Article ID 197978, 11 pages
Research Article

On a Coupled System of Shallow Water Equations Admitting Travelling Wave Solutions

1Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
2Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, 06123 Perugia, Italy
3Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Received 20 January 2015; Accepted 25 March 2015

Academic Editor: Robert A. Van Gorder

Copyright © 2015 D. Burini 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.


We consider three inviscid, incompressible, irrotational fluids that are contained between the rigid walls and and that are separated by two free interfaces and . A generalized nonlocal spectral (NSP) formulation is developed, from which asymptotic reductions of stratified fluids are obtained, including coupled nonlinear generalized Boussinesq equations and -dimensional shallow water equations. A numerical investigation of the -dimensional case shows the existence of solitary wave solutions which have been investigated for different values of the characteristic parameters.