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Article overview
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Evolution of solitary waves and undular bores in shallow-water flows
over a gradual slope with bottom friction | G.A. El
; R.H.J. Grimshaw
; A.M. Kamchatnov
; | Date: |
31 Mar 2007 | Subject: | nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems) | Abstract: | This paper considers the propagation of shallow-water solitary and nonlinear
periodic waves over a gradual slope with bottom friction in the framework of a
variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging
method, using a recent development of this theory for perturbed integrable
equations. This general approach enables us not only to improve known results
on the adiabatic evolution of isolated solitary waves and periodic wave trains
in the presence of variable topography and bottom friction, modeled by the
Chezy law, but also importantly, to study the effects of these factors on the
propagation of undular bores, which are essentially unsteady in the system
under consideration. In particular, it is shown that the combined action of
variable topography and bottom friction generally imposes certain global
restrictions on the undular bore propagation so that the evolution of the
leading solitary wave can be substantially different from that of an isolated
solitary wave with the same initial amplitude. This non-local effect is due to
nonlinear wave interactions within the undular bore and can lead to an
additional solitary wave amplitude growth, which cannot be predicted in the
framework of the traditional adiabatic approach to the propagation of solitary
waves in slowly varying media. | Source: | arXiv, arxiv.0704.0045 | Services: | Forum | Review | PDF | Favorites |
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