Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadata

Cited literature [48 references]  Display  Hide  Download
Contributor : Denys DUTYKH Connect in order to contact the contributor
Submitted on : Wednesday, April 10, 2019 - 10:01:59 AM
Last modification on : Wednesday, November 3, 2021 - 6:17:37 AM
Long-term archiving on: : Thursday, July 11, 2019 - 3:12:50 PM


Files produced by the author(s)


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License




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⟩



Record views


Files downloads