On some localized waves described by the extended KdV equation

Alexey V. Porubov; Gérard A. Maugin; Vitaly V. Gursky; Valeria V. Krzhizhanovskaya

doi:10.1016/j.crme.2005.06.003

On some localized waves described by the extended KdV equation
[Sur quelques ondes localisées gouvernées par une équation de KdV généralisée]

Présenté par : Évariste Sanchez-Palencia

Alexey V. Porubov ¹ ; Gérard A. Maugin ² ; Vitaly V. Gursky ¹ ; Valeria V. Krzhizhanovskaya ³

¹ Ioffe Physico-Technical Institute of the Russian Academy of Sciences, St. Petersburg 194021, Russia
² Laboratoire de modélisation en mécanique associé au CNRS, université Pierre et Marie Curie, 4, place Jussieu, case 162, 75252 Paris cedex 05, France
³ Institute for High-Performance Computing and Data Bases, St.Petersburg, Russia

Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 528-533.

Résumé
Abstract

On étudie l'influence des termes non linéaires d'ordre élevé sur la forme d'ondes solitaires dans des systèmes mécaniques gouvernés par une équation de KdV d'ordre cinq. On montre que de nouvelles solutions d'ondes localisées présentant des oscillations intrinsèques (pas des ‘breathers’) sont engendrées par une impulsion initiale arbitraire grâce aux non linéarités quadratiques, alors que la non linéarité cubique est responsable de la formation d'une onde solitaire dite « épaisse » (ou « grasse »).

The influence of higher-order nonlinear terms on the shape of solitary waves is studied for mechanical systems governed by a generalization of the 5th order Korteweg–de Vries equation. New localized travelling wave with intrinsic oscillations (not breathers) is shown to arise from arbitrary initial pulse thanks only to the higher-order quadratic nonlinearity, while cubic nonlinearity is responsible for the formation of so-called ‘fat’ solitary wave.

Reçu le : 2004-10-06
Accepté le : 2005-06-14
Publié le : 2005-07-01

DOI : 10.1016/j.crme.2005.06.003

Keywords: Waves, Nonlinear wave, Solitary wave, Numerical solution
Mot clés : Ondes, Ondes non linéaires, Ondes solitaires, Solution numérique

Affiliations des auteurs :

Alexey V. Porubov ¹ ; Gérard A. Maugin ² ; Vitaly V. Gursky ¹ ; Valeria V. Krzhizhanovskaya ³

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     author = {Alexey V. Porubov and G\'erard A. Maugin and Vitaly V. Gursky and Valeria V. Krzhizhanovskaya},
     title = {On some localized waves described by the extended {KdV} equation},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {528--533},
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     year = {2005},
     doi = {10.1016/j.crme.2005.06.003},
     language = {en},
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Alexey V. Porubov; Gérard A. Maugin; Vitaly V. Gursky; Valeria V. Krzhizhanovskaya. On some localized waves described by the extended KdV equation. Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 528-533. doi : 10.1016/j.crme.2005.06.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.06.003/

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