  In this paper we show that non-smooth functions which are distributional
traveling wave solutions to the two component Camassa-Holm equation are
distributional traveling wave solutions to the Camassa-Holm equation provided
that the set $u^{-1}(c)$, where $c$ is the speed of the wave, is of measure
zero. In particular there are no new peakon or cuspon solutions beyond those
already satisfying the Camassa-Holm equation. However, the two component
Camassa-Holm equation has distinct from Camassa-Holm equation smooth traveling
wave solutions as well as new distributional solutions when the measure of
$u^{-1}(c)$ is not zero. We provide examples of such solutions.
