Demodulation of Pulsed Acoustic Signals in Strongly Nonlinear Propagation Regimes

A one-dimensional nonlinear problem of parametric generation of low-frequency radiation is considered in the case of a pulsed high-frequency initial excitation capable of forming shock fronts in the wave profile. A numerical algorithm for solving the Burgers equation in the time domain using a Godunov-type shock-capturing scheme is developed. Examples of the propagation of model frequency-modulated signals with different envelope shapes at different ratios of nonlinear and dissipative effects, which limit the interaction length of pump waves, are considered. Examples of the evolution of waveforms and spectra in a process of self-demodulation of a high-frequency pump signal are given, with self-demodulation manifesting at shorter distances in strongly nonlinear propagation regimes due to additional attenuation of wave energy at shock fronts. It is shown that the efficiency of low-frequency generation increases in shockwave propagation regimes.