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

Denys Dutykh, Delia Ionescu-Kruse

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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–Itō 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–Itō 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.

Original languageBritish English
Pages (from-to)5521-5541
Number of pages21
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number9
StatePublished - Sep 2019


  • Analytical solutions
  • Camassa–Holm equations
  • Cnoidal waves
  • Kaup–Boussinesq equations
  • Multi-pulsed solutions
  • Phase-plane analysis
  • Solitary waves
  • Waves on shear flow
  • Zakharov–Ito system


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