Self-switching of waves in materials

The problem is formulated on self-switching of acoustic waves in materials when the wavelength does not exceed considerably the representative dimension of the microstructure. Use is made of the microstructural theory of two-component mixtures, which is adapted well to study waves in composites. Truncated and evolutionary equations describing the interaction of two longitudinal plane waves - a strong pumping wave and a weak signal wave - are derived. A procedure of finding the exact solution to the evolutionary equations is described for the case where the wave numbers of the pumping and signal waves are equal. The solution is expressed in terms of the elliptic Jacobi function.