Abstract
High-frequency transverse electromagnetic waves in a collisionless isotropic dusty plasma damp via nonlinear Landau damping. Taking into account the latter we have obtained a generalized set of Zakharov equations with local and nonlocal terms. Then from this coupled set of Zakharov equations a kinetic nonlinear Schrödinger equation with local and nonlocal nonlinearities is derived for special cases. It is shown that the modulation of the amplitude of the electromagnetic waves leads to the modulation instability through the nonlinear Landau damping term. The maximum growth rate is obtained for the special case when the group velocity of electromagnetic waves is close to the dust acoustic velocity.
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