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Dispersive Nonlinear Shallow‐Water Equations
Author(s) -
Antuono M.,
Liapidevskii V.,
Brocchini M.
Publication year - 2009
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2008.00422.x
Subject(s) - nonlinear system , hyperbolic partial differential equation , mathematics , mathematical analysis , shallow water equations , representation (politics) , dispersive partial differential equation , boussinesq approximation (buoyancy) , waves and shallow water , set (abstract data type) , interpretation (philosophy) , physics , partial differential equation , mechanics , thermodynamics , convection , natural convection , quantum mechanics , politics , political science , rayleigh number , law , computer science , programming language
A set of dispersive and hyperbolic depth‐averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq‐type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive and nonlinear wave phenomena. A detailed description of the conditioning of the dispersive terms and a physical interpretation of the hyperbolic approximation is provided. The dispersive and hyperbolic structure of the new set of equations is analyzed in depth and an analytical solitary‐wave solution is found.