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.
Domains
Fluid mechanics [physics.class-ph] Fluid Dynamics [physics.flu-dyn] Classical Analysis and ODEs [math.CA] Mathematical Physics [math-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS] Analysis of PDEs [math.AP] Dynamical Systems [math.DS] Mathematical Physics [math-ph] Algebraic Geometry [math.AG]Origin | Files produced by the author(s) |
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