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Nonlinear interaction of electrostatic surface waves in a semi-infinite plasma. Part 1. Derivation of the coupled mode equations

We have derived a set of coupled mode equations which govern the nonlinear interaction of three high-frequency electrostatic surface waves through a low-frequency density perturbation produced by them. The set is compared with that obtained when a similar problem is solved for bulk waves in an infinite plasma. Some differences are shown to exist caused by the specific features of surface waves such as the amplitude attenuation normal to the interface and their hybrid nature.