Localization in optical systems with an intensity-dependent dispersion

TL;DR

This paper investigates the existence and properties of solitary waves in nonlinear optical systems with intensity-dependent dispersion, revealing conditions for their existence and analyzing their stability and characteristics.

Contribution

It provides a rigorous proof of the non-existence of solitary waves under certain conditions and characterizes a family of solutions including cusped and bell-shaped solitons.

Findings

No solitary waves exist when the signs of dispersion match.

A family of solitary waves exists when signs are opposite.

Numerical analysis supports the analytical results.

Abstract

We address the nonlinear Schrodinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if the sign of the intensity-dependent dispersion coincides with the sign of the constant dispersion, whereas a continuous family of such solutions exists in the case of the opposite signs. The family includes two particular solutions, namely cusped and bell-shaped solitons, where the former represents the lowest energy state in the family and the latter is a limit of solitary waves in a regularized system. We further analyze the delicate analytical properties of these solitary waves such as the asymptotic behavior near singularities, the spectral stability, and the convergence of the fixed-point iterations near such solutions. The analytical theory is corroborated by means of numerical approximations.