# Scalar and vector electromagnetic solitary waves in nonlinear hyperbolic media

## TL;DR

This paper explores the propagation of electromagnetic solitary waves in hyperbolic nonlinear media, deriving exact solutions and analyzing how hyperbolic dispersion influences wave stability and unique propagation characteristics.

## Contribution

It provides analytical solutions for scalar and vector solitary waves in hyperbolic nonlinear media, highlighting the role of hyperbolic dispersion in wave stability and preventing singularities.

## Key findings

- Hyperbolic dispersion adds a degree of freedom to control wave singularities.
- Exact analytical forms of solitary waves are derived using Hirota bilinear method.
- Solitary waves exhibit unique propagation properties not seen in conventional media.

## Abstract

In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider the scalar hyperbolic nonlinear Schr\"odinger system and its coupled version, namely hyperbolic Manakov type equations. These hyperbolic systems are shown to be non-integrable. Then, we examine the propagation properties of both the scalar and vector electromagnetic solitary waves by deriving their exact analytical forms through the Hirota bilinear method. A detailed analysis shows that the presence of hyperbolic transverse 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 realize 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.