The propagation of solitary waves in piezoelectric semiconductors

A non-linear theory of the propagation of acoustic waves in piezoelectric semiconductors is presented, based on an asymptotic expansion in multiple time and space scales. The envelope of the wave amplitude is found to satisfy a non-linear Schrodinger equation with complex coefficients. The solution of this equation is obtained using a perturbation technique. This result, a solitary wave, is used to study the saturation of the instability and it is found that the saturation mechanism is a local change of d.c. electric field and carrier concentration.