A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation

Samer Israwi; Henrik Kalisch

doi:10.5802/crmath.143

Équations aux dérivées partielles

A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation

Samer Israwi ¹ ; Henrik Kalisch ²

¹ Lebanese University, Faculty of Sciences 1, Department of Mathematics, Hadath-Beirut, Lebanon
² Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway

Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 39-45.

Résumé
Abstract

L’équation de KdV est considérée comme un modèle approximatif pour des ondes longues de faible amplitude à la surface libre d’un fluide non visqueux. On montre qu’il y a une densité de moment approximative associée à l’équation de KdV, et que la différence entre cette densité et la densité de de moment physique dérivée dans le contexte du système d’Euler peut être estimée en fonction du paramètre d’onde longue.

Consideration is given to the KdV equation as an approximate model for long waves of small amplitude at the free surface of an inviscid fluid. It is shown that there is an approximate momentum density associated to the KdV equation, and the difference between this density and the physical momentum density derived in the context of the full Euler equations can be estimated in terms of the long-wave parameter.

Reçu le : 2018-08-16
Révisé le : 2020-11-02
Accepté le : 2020-11-02
Publié le : 2021-03-01

DOI : 10.5802/crmath.143

Affiliations des auteurs :

Samer Israwi ¹ ; Henrik Kalisch ²

¹ Lebanese University, Faculty of Sciences 1, Department of Mathematics, Hadath-Beirut, Lebanon
² Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Samer Israwi and Henrik Kalisch},
     title = {A {Mathematical} {Justification} of the {Momentum} {Density} {Function} {Associated} to the {KdV} {Equation}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {39--45},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {1},
     year = {2021},
     doi = {10.5802/crmath.143},
     language = {en},
}

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Samer Israwi; Henrik Kalisch. A Mathematical Justification of the Momentum Density Function Associated to the KdV Equation. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 39-45. doi : 10.5802/crmath.143. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.143/

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