Theory of the surface acoustic soliton. II. Semiconducting solid

A theory of the surface acoustic soliton in a semiconductor is presented based on the coherent-state representation of the equation of motion for the surface phonons interacting with the conduction electrons. It is shown that the two-dimensional displacement field satisfies the nonlinear integro-differential equation with a damping term. With the aid of the reductive perturbation method, the equation can be reduced to the nonlinear Schr\"odinger equation with a damping term whose coefficient is the attenuation rate of the surface phonon. The approximate solution is derived to reveal excellent agreement with the numerical result.