Solitons supported by localized parametric gain

TL;DR

This paper investigates the existence, stability, and properties of one-dimensional solitons supported by localized parametric gain in nonlinear media, providing analytical solutions and stability analysis for different soliton types.

Contribution

It introduces the concept of localized parametric gain supporting various solitons and provides analytical solutions along with stability analysis in focusing and defocusing media.

Findings

Fundamental solitons are partly stable in focusing media and fully stable in defocusing media.

Higher-order solitons are unstable.

Existence thresholds and a stable exact solution are analytically derived.

Abstract

We address the existence and properties of one-dimensional solitons maintained by localized parameter gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order solitons are unstable. In addition to numerical results, the existence threshold for the solitons, and a particular stable exact solution are obtained in an exact analytical form.