Solitons in a medium with linear dissipation and localized gain

TL;DR

This paper explores the existence and properties of dissipative solitons and breathing modes in a medium with localized gain and linear dissipation, revealing unique localization and stability features.

Contribution

It introduces new types of dissipative solitons and breathing modes in media with localized gain and dissipation, highlighting their unusual properties and stability conditions.

Findings

Existence of exponentially localized modes in both focusing and defocusing media

Stable symmetric and anti-symmetric localized modes with dual gain maxima

Presence of stable breathing solutions in the system

Abstract

We present a variety of dissipative solitons and breathing modes in a medium with localized gain and homogeneous linear dissipation. The system posses a number of unusual properties, like exponentially localized modes in both focusing and defocusing media, the existence of modes in focusing media at negative propagation constant values, the simultaneous existence of stable symmetric and anti-symmetric localized modes when the gain landscape possesses two local maxima, as well as the existence of stable breathing solutions.