The Decay of Pulses with Complex Structure According to Burgers' Equation

Nonlinear plane acoustic waves propagating through a fluid are studied using Burgers' equation with the viscosity tending to zero. The evolution of initial pulses with monochromatic and noise carrier is considered. The initial pulses are characterized by two length scales. The length scale for substantial changes of the modulation function is much greater than the corresponding scale of the carrier. Some simple pulses with only one length scale are also studied since their properties are important for the studies of pulses with two scales. With increasing time the initial pulses are deformed and shocks appear. The shocks then merge and finally a finite pulse ends up with an N-wave and a periodic signal with a sawtooth wave. It is investigated how the characteristics of the final waves depends on the characteristics of the initial waves. Both numerical and analytical methods are used.