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
Contributor : Denys Dutykh
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Submitted on : Tuesday, March 29, 2016 - 3:10:19 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
Document(s) archivé(s) le : Thursday, June 30, 2016 - 4:34:29 PM
