The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
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Date
2011
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Abstract
The Serre equations are a pair of strongly nonlinear, weakly dispersive, Boussinesq-type partial differential equations. They model the evolution of the surface elevation and the depth-averaged horizontal velocity of an inviscid, irrotational, incompressible, shallow fluid. They admit a three-parameter family of cnoidal wave solutions with improved kinematics when compared to KdV theory. We examine their linear stability and establish that waves with sufficiently small amplitude/steepness are stable while waves with sufficiently large amplitude/steepness are unstable. (C) 2010 Elsevier Masson SAS. All rights reserved.
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Serre, Stability, Kinematics, Nonlinear, BOUSSINESQ-TYPE EQUATIONS, KORTEWEG-DEVRIES EQUATION, FINITE-VOLUME SCHEME, DE-VRIES EQUATION, LINEAR-STABILITY, WATER-WAVES, LONG WAVES, DERIVATION, SHALLOW, MODEL