Travelling wave solutions for some two-component shallow water models

21 pages, 13 figures, 37 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/International audienceIn 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