Dispersion of nonlinearity, nonlinear dispersion, and absorption of sound in micro-inhomogeneous materials

New evolution equations for nonlinear acoustic waves in micro-inhomogeneous media, which take into account relaxation processes, are derived. The proposed theory provides the description of such physical effects as frequency-dependent nonlinear absorption of sound, nonlinearity of its velocity dispersion, and dispersion of the nonlinear acoustic parameters of micro-inhomogeneous materials. The theory predicts that, depending on the ratio of the characteristic relaxation time to the wave period, nonlinearity can grow or diminish with increasing frequency, while an increase in wave amplitude can lead to a rise or fall of the propagation velocity. In the limiting cases where the relaxation processes are instantaneous or quasi-frozen, analytical solutions of the nonlinear equations are found and analyzed. (C) 1998 Acoustical Society of America.