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Journal Articles Journal of Differential Equations Year : 2016

Travelling wave solutions for some two-component shallow water models

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.
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Dates and versions

hal-01294603 , version 1 (29-03-2016)

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Attribution - NonCommercial - NoDerivatives

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Denys Dutykh, Delia Ionescu-Kruse. Travelling wave solutions for some two-component shallow water models. Journal of Differential Equations, 2016, 261 (2), pp.1099-1114. ⟨10.1016/j.jde.2016.03.035⟩. ⟨hal-01294603⟩
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