Amplitude-dependent internal friction and harmonics generation in solids with histeretic nonlinearity

Theoretical and numerical study of nonlinear wave processes in media with hysteretic nonlinearity are carried out. The phenomena of amplitude-dependent damping as well as change of the propagation velocity of harmonic wave and its second and third harmonic generation are considered. It was shown that the hysteretic media possess nonlinear dispersion that become apparent in the difference between the phase velocities of strong harmonic pump wave and its weak high harmonics. The dispersion leads to both spatial beatings and non-monotonically rate of growth of an amplitude of high harmonic at the increase in amplitude of basic frequency wave.