This Note investigates the effect of a renormalization technique on high-order shallow water approximations of gravity waves. The method is illustrated for the solitary surface wave. Applied to the solution of a generalized KdV equation, it is shown that the renormalization significantly increases the accuracy.
On traite de l'effet d'une technique de renormalisation sur les approximations d'ordres supérieurs de type eau peu profonde pour les ondes de gravité. La méthode est illustrée pour l'onde solitaire. En renormalisant la solution d'une équation KdV généralisée, il est montré que la précision s'en trouve grandement augmentée.
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Mots-clés : Ondes, Eau peu profonde, Onde solitaire, Renormalisation
Didier Clamond 1; Dorian Fructus 1
@article{CRMECA_2003__331_11_727_0, author = {Didier Clamond and Dorian Fructus}, title = {Accurate simple approximation for the solitary wave}, journal = {Comptes Rendus. M\'ecanique}, pages = {727--732}, publisher = {Elsevier}, volume = {331}, number = {11}, year = {2003}, doi = {10.1016/j.crme.2003.09.001}, language = {en}, }
Didier Clamond; Dorian Fructus. Accurate simple approximation for the solitary wave. Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 727-732. doi : 10.1016/j.crme.2003.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.09.001/
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