On a coupled system of shallow water equations admitting travelling wave solutions
type: Item
instance of: scholarly article
title: On a coupled system of shallow water equations admitting travelling wave solutions
zbMATH Open document ID: 1394.35350
DOI: 10.1155/2015/197978
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: We consider three inviscid, incompressible, irrotational fluids that are contained between the rigid walls \(y = - h_1\) and \(y = h + H\) and that are separated by two free interfaces \(\eta_1\) and \(\eta_2\). A generalized nonlocal spectral (NSP) formulation is developed, from which asymptotic reductions of stratified fluids are obtained, including coupled nonlinear generalized Boussinesq equations and \((1 + 1)\)-dimensional shallow water equations. A numerical investigation of the \((1 + 1)\)-dimensional case shows the existence of solitary wave solutions which have been investigated for different values of the characteristic parameters.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6925740
Wikidata QID: Q59117574
author: Diletta Burini
author: S. De Lillo
author: D. Skouteris
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/197978
OpenAlex ID: W1629179125
cites work: Available potential energy and mixing in density-stratified fluids
cites work: LONG NONLINEAR INTERNAL WAVES
cites work: Internal waves of permanent form in fluids of great depth
cites work: Algebraic solitary waves in stratified fluids
cites work: Lagrange multiplier formalism for a spin-3/2 field
cites work: Fully nonlinear internal waves in a two-fluid system
cites work: Weakly nonlinear internal waves in a two-fluid system
cites work: Hamiltonian long‐wave expansions for free surfaces and interfaces
cites work: On a new non-local formulation of water waves
cites work: On the integrability of linear and nonlinear partial differential equations
cites work: A reformulation and applications of interfacial fluids with a free surface
cites work: Q3094853
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description: scientific article; zbMATH DE number 6925740