Propagation of Acoustics Waves of Nonsimplex Form in a Material With Hysteretic Quadratic Nonlinearity: Analysis and Numerical Simulations

The numerical scheme for the analysis of the acoustic wave transformation in materials with nonlinearity hysteresis and end-point memory is developed. Both numerical and analytical predictions are obtained concerning mixing of a wave at fundamental frequency (ω-wave) and a wave at doubled frequency (2ω-wave) in the materials with hysteretic quadratic nonlinearity. The observed wave spectrum broadening is found to be in qualitative agreement with the selection rules for the multi-phonon processes in this type of materials. The predicted transformation of an initially complex wave (with four extrema over a period) into a simplex wave (with two extrema over a period) in nonlinear propagation is found to be one of the manifestations of the nonlinear hysteretic absorption. It is demonstrated that at short propagation distances the interaction of the ω- and 2ω-waves is mainly through the mechanism of the nonlinear hysteretic absorption and is not strongly influenced by the process of higher harmonics generation and their inverse influence on the input waves. The regimes of the induced and self-induced transparency are predicted. The influence of the transition from the simplex wave to complex wave emission (or vice versa) on the processes of the induced absorption and transparency is identified.