Arc-shaped solitons on a gain-loss ring

We address the properties of arc-shaped solitons supported by defocusing nonlinearity on a partially-parity-time symmetric ring, including the existence and stability. Four types of arc-shaped solitons are found. The existence region of arc-shaped solitons with two or more bright spots is the same, while it is slightly smaller in value than that of fundamental solitons. Also, the existence domains of arc-shaped solitons shrink with the increase of the strength of the gain and loss term. At moderate gain and loss levels, stable arc-shaped solitons are usually localized in the middle of their existence domain. The characteristics of unstable arc-shaped solitons are considered to be related to the power-flow of the solitons, because the sidelobes of solitons extend to multiple Gaussian waveguides at both ends of their existence, and then not all the power-flows in each Gaussian waveguide flow from the gain to the loss region. Otherwise, robust nonlinear arc-shaped states with four different bright spots can be excited by Gaussian beams. This work offers us new insight and understanding of optical solitons on a partially-parity-time symmetric ring.