Abstract:

The incentive for this work was to determine when and how the information in a nonlinear signal disappears when propagating. This may be done by backpropagating the evolution and comparing the back-traced signal with the original one. The Burgers equation is investigated for both the nondissipative and dissipative cases. For a nondissipative evolution the wave completely coincides with the original one when shocks have not formed, while only part of it coincides after shock formation. Although the wave no longer contains the original information, except for the original signals with all derivatives continuous, parts of the wave theoretically carry all the information. These parts grow smaller and smaller, and thus a problem lies in the numerical accuracy which sometimes causes several different signals conform, and in that way the wave in practice has lost information. A semi-analytical model has been developed which automatically determines the distance to be backpropagated for modulated waves and gives one or more alternatives for the original signal. This may be used as a signal processing tool. [Work supported by TFR, the Swedish Research Council for Engineering Sciences.]