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Numerical study of a family of dissipative KdV equations

Jean-Paul Chehab 1, 2, * Georges Sadaka 1
* Corresponding author
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : The weak damped and forced KdV equation on the 1d Torus on $[0,L]$ have been analyzed by Ghidaglia\cite{Gh1,Gh2} Goubet\cite{G,GR}, Rosa and Cabral \cite{cabral-rosa} and asymptotic regularization effects have been proven and observed numerically. In this work, we consider a family of dampings that can be even weaker, particularly it can dissipate very few the high frequencies. We give here numerical evidences that point out dissipation of energy, regularization effect, and presence of special solutions that characterize a non trivial dynamics (steady states, time periodic solutions).
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Submitted on : Monday, February 21, 2011 - 4:10:02 PM
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Jean-Paul Chehab, Georges Sadaka. Numerical study of a family of dissipative KdV equations. [Technical Report] 2011, pp.77. ⟨inria-00529227v2⟩

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