Formation of caustics in k-essence and Horndeski theory

We study propagation of waves and appearance of caustics in k-essence and galileon theories. first we show that previously known solutions for travelling waves in k-essence and galileon models correspond to very specific fine-tuned initial conditions. on the contrary, as we demonstrate by the method of characteristics, generic initial conditions leads to a wave in k-essence which ends up with formation of caustics. finally, we find that any wave solution in pure k-essence is also a solution for a galileon theory with the same k-essence term. thus in the horndeski theory with a k-essence term formation of caustics is generic. we discuss physical consequences of the caustics formation and possible ways to cure the problem.