  We consider the CH-KP-I equation. For this equation we prove the existence of
steady solutions, which are solitary in one horizontal direction and periodic
in the other. We show that such waves bifurcate from the line solitary wave
solutions, i.e. solitary wave solutions to the Camassa-Holm equation, in a
dimension-breaking bifurcation. This is achieved through reformulating the
problem as a dynamical system for a perturbation of the line solitary wave
solutions, where the periodic direction takes the role of time, then applying
the Lyapunov-Iooss theorem.
