Two-dimensional dissipative solitons supported by localized gain

TL;DR

This paper demonstrates that a balance between localized gain and nonlinear dissipation in a 2D nonlinear Schrödinger equation enables stable, non-collapsing solitons that exhibit symmetry breaking at higher gain levels.

Contribution

It introduces a new mechanism for stable 2D dissipative solitons supported by localized gain and nonlinear dissipation, including symmetry-breaking phenomena.

Findings

Stable 2D dissipative solitons exist under certain gain conditions.

Solitons do not undergo diffraction or collapse.

Symmetry breaking occurs at high gain levels.

Abstract

We show that the balance between localized gain and nonlinear cubic dissipation in the twodimensional nonlinear Schrodinger equation allows for existence of stable two-dimensional localized modes which we identify as solitons. Such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. The observed solitons neither undergo diffractive spreading nor collapse. Above the critical value of the gain the symmetry breaking occurs and asymmetric dissipative solitons emerge.