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Effects of vorticity on the travelling waves of some shallow water two-component systems

Abstract : In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations, the Zakharov-Ito system and the Kaup--Boussinesq equations all including constant vorticity effects. We analyze both solitary and periodic-type travelling waves using the simple and geometrically intuitive phase space analysis. We get the pulse-type solitary wave solutions and the front solitary wave solutions. For the Zakharov-Ito system we underline the occurrence of the pulse and anti-pulse solutions. The front wave solutions decay algebraically in the far field. For the Kaup-Boussinesq system, interesting analytical multi-pulsed travelling wave solutions are found.
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https://hal.archives-ouvertes.fr/hal-02094922
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Denys Dutykh, Delia Ionescu-Kruse. Effects of vorticity on the travelling waves of some shallow water two-component systems. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2019, 39 (9), pp.5521-5541. ⟨10.3934/dcds.2019225⟩. ⟨hal-02094922⟩

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