Theory of the surface acoustic soliton. I. Insulating solid

Starting from the equation of motion for anharmonically interacting surface phonons, a theory of the surface acoustic soliton in an insulating solid is developed, based on the coherent-state representation. The two-dimensional nonlinear integro-differential equation for the classical displacement field is obtained. By using the reductive perturbation method, the equation can be reduced to the nonlinear Schr\"odinger equation, which allows the existence of the surface acoustic soliton of the envelope type. The possibility of observing the surface acoustic soliton is also discussed.