Time reversing solitary waves.
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 forcing the 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 new Boussinesq model, both in transmission and in reflection.
Fouque
Jean-Pierre
JP
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, USA.
Garnier
Josselin
J
Muñoz Grajales
Juan Carlos
JC
Nachbin
André
A