Propagation of electromagnetic waves in a nonlinear hyperbolic medium

The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial is considered. Without taking into account the dispersion of group velocities, the propagation of a wave in such a medium can be described either by the hyperbolic nonlinear Schrödinger equation or by the hyperbolic Manakov equations. It is shown that in contrast to the case of ordinary media, the region in the space of wave vectors, in which the modulation instability of a spatially homogeneous wave is possible, is not limited.