Propagation of Electromagnetic Waves in a Nonlinear Hyperbolic Medium

We consider propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial. If the dispersion of group velocities is neglected, wave propagation in such a medium can be described either by a hyperbolic nonlinear Schrodinger equation or by hyperbolic Manakov equations. It is shown that the region in the space of wave vectors in which modulation instability of a spatially homogeneous wave is possible is not limited, in contrast to the case of ordinary media.