Abstract : In the present study we perform a unified analysis of travelling wave solutions to three different two-component systems which appear in shallow water theory. Namely, we analyse the celebrated Green-Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models.
In particular, we show the existence of new type of solutions.
https://hal.archives-ouvertes.fr/hal-01294603
Contributeur : Denys Dutykh
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Soumis le : mardi 29 mars 2016 - 15:10:19
Dernière modification le : jeudi 11 janvier 2018 - 06:12:26
Document(s) archivé(s) le : jeudi 30 juin 2016 - 16:34:29
