Gyrating solitons in a necklace of optical waveguides

We consider light pulses in a circular array of $2N$ coupled nonlinear optical waveguides. The waveguides are either hermitian or alternate gain and loss in a $\mathcal{PT}$-symmetric fashion. Simple patterns in the array include a ring of $2N$ pulses travelling abreast, and a breather -- a string of pulses where all even and all odd waveguides flash in turn. In addition, the structure displays solitons gyrating around the necklace by switching from one waveguide to the next. Some of the gyrating solitons are stable while other ones are weakly unstable and evolve into gyrating multiflash strings. By tuning the gain-loss coefficient, the gyration of solitons in a nonhermitian array may be reversed without changing the direction of their translational motion.