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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Denys Dutykh, Delia Ionescu-Kruse. Travelling wave solutions for some two-component shallow water models. Journal of Differential Equations, Elsevier, 2016, 261 (2), pp.1099-1114. 〈http://www.sciencedirect.com/science/article/pii/S0022039616300110〉. 〈10.1016/j.jde.2016.03.035〉. 〈hal-01294603〉

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