The following two-component generalization of the Camassa-Holm equation is considered
where , , for real parameters.
The existence of solitary wave solutions (homoclinic orbits), kink and anti-kink wave solutions (heteroclinic orbits) and periodic wave solutions is investigated by using a dynamical systems approach. Some exact explicit parametric representations of travelling wave solutions are provided too.
Finally, the existence of uncountably infinite many breaking wave solutions (whose maximal existence interval is bounded) is proved for .