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

## TL;DR

This paper investigates how vorticity influences travelling wave solutions in several shallow water models, revealing new solitary, pulse, and front wave solutions through phase space analysis.

## Contribution

It introduces analysis of vorticity effects on both integrable and non-integrable shallow water systems, identifying new wave solutions.

## Key findings

- Pulse-type solitary wave solutions identified
- Front solitary waves decay algebraically
- Multi-pulsed travelling wave solutions found in Kaup-Boussinesq system

## 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.