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.
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 »).
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Mots-clés : Ondes, Ondes non linéaires, Ondes solitaires, Solution numérique
Alexey V. Porubov 1; Gérard A. Maugin 2; Vitaly V. Gursky 1; Valeria V. Krzhizhanovskaya 3
@article{CRMECA_2005__333_7_528_0, 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}, publisher = {Elsevier}, volume = {333}, number = {7}, year = {2005}, doi = {10.1016/j.crme.2005.06.003}, language = {en}, }
TY - JOUR AU - Alexey V. Porubov AU - Gérard A. Maugin AU - Vitaly V. Gursky AU - Valeria V. Krzhizhanovskaya TI - On some localized waves described by the extended KdV equation JO - Comptes Rendus. Mécanique PY - 2005 SP - 528 EP - 533 VL - 333 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2005.06.003 LA - en ID - CRMECA_2005__333_7_528_0 ER -
%0 Journal Article %A Alexey V. Porubov %A Gérard A. Maugin %A Vitaly V. Gursky %A Valeria V. Krzhizhanovskaya %T On some localized waves described by the extended KdV equation %J Comptes Rendus. Mécanique %D 2005 %P 528-533 %V 333 %N 7 %I Elsevier %R 10.1016/j.crme.2005.06.003 %G en %F CRMECA_2005__333_7_528_0
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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