Shock structure due to stochastic forcing and the time reversal of nonlinear waves

This paper is concerned with the study of the deformation of a nonlinear pulse traveling in a random medium. We consider shallow water waves with a spatially random depth. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear conservation law is regularized leading to a viscous shock profile. This enables us to perform time-reversal experiments beyond the critical time for shock formation.