A Note on Traveling Wave Solutions to the Two Component Camassa–Holm Equation

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