Scalar and vector electromagnetic solitary waves in nonlinear hyperbolic media

In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider a scalar hyperbolic nonlinear Schr\"odinger system and its coupled version. We examine the propagation properties of both the scalar and vector solitary waves by deriving their exact analytical forms through the Hirota bilinear method. A detailed analysis shows that the presence of hyperbolic dispersion provides an additional degree of freedom to prevent the formation of singularity in both the scalar and vector solitary wave structures in this hyperbolic nonlinear media. Besides this, we also exhibit that the solitary waves in this media possess fascinating propagation properties which cannot be observed in conventional nonlinear media. We believe that the present study will be very useful in analyzing electromagnetic wave propagation in hyperbolic nonlinear metamaterials.