A theory of the surface acoustic soliton in superlattices is presented. Starting from the equation of motion for interacting surface phonons in superlattices, the two-dimensional nonlinear wave equation for the classical displacement is obtained based on the coherent-state representation of the surface phonons. The equation can be reduced to the nonlinear Schr\"odinger equation with a dissipation term by means of the reductive perturbation method. The dispersion relation of the surface phonons which plays an essential role to the modulational instability is also investigated for some typical structures of superlattices.
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Sakuma et al. (1987) studied this question.
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