Time reversing solitary waves
Andre Nachbin | Fouque, Jean-Pierre | Garnier, Josselin | Munoz Grajales, Juan Carlos
nonlinear waves | solitary waves | inhomogeneous media | time reversal
We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcingthe solution to the nonlinear (shallow water) conservation law is regularized leading to a viscous shock profile. This enables time-reversal experiments beyond the critical time for shock formation. Furthermore we present numerical experiments for the time reversed refocusing of solitary waves in a regime where theory is not yet available. Solitary wave refocusing simulations are performed with a Boussinesq model, both in transmission and in reflection.