Symmetry breaking and multi-hump solitons in inhomogeneous gain landscapes

TL;DR

This paper investigates how inhomogeneous gain landscapes influence one-dimensional soliton formation in nonlinear media, revealing symmetry breaking and multi-hump structures depending on the number of gain channels.

Contribution

It introduces the concept that the number of amplifying channels determines the symmetry and stability of solitons in inhomogeneous gain landscapes.

Findings

Symmetry breaking occurs via pitchfork bifurcation with increasing gain.

Odd number of channels allows multiple co-existing stable modes.

Even number of channels results only in asymmetric stable states.

Abstract

We address one-dimensional soliton formation in the cubic nonlinear medium with two-photon absorption and transversally inhomogeneous gain landscape consisting of a single or several amplifying channels. Existence of the solitons requires certain threshold gain while the properties of solitons strongly depend on whether the number of the amplifying channels is odd or even. In the former case an increase of the gain leads to a symmetry breaking, which occurs through the pitchfork bifurcation, and to emergence of a single or several co-existing stable asymmetric modes. In the case of even number of amplifying channels we have found only asymmetric stable states.