Exact identity for nonlinear wave propagation.
An exact identity for nonlinear sound wave propagation in one-dimensional media is shown to apply under a wide variety of conditions. The evidence suggests that this is true whenever there is a single input and output channel on each side of the medium, which can generally be achieved using monochromatic filters. It is shown mathematically that the identity cannot be derived from this condition and the known symmetries of the system. The question of what hidden symmetries in the system lead to the identity, and whether it applies even more generally to light waves, remains unresolved.
Ralph
Duncan
D
Department of Physics, University of California, Santa Cruz, California 95064, USA.
Narayan
Onuttom
O
Montgomery
Richard
R