We show that Kerr beam self-cleaning results from parametric mode mixing instabilities, that generate a number of nonlinearly interacting modes with randomised phases -optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is analogue to wave condensation that is well-known in hydrodynamic 2D turbulence.

We investigate the application of dynamic deep neural networks for nonlinear equalization in long haul transmission systems. Through extensive numerical analysis we identify their optimum dimensions and calculate their computational complexity as a function of system length. Performing comparison with traditional back-propagation based nonlinear compensation of 2 steps-per-span and 2 samples-per-symbol, we demonstrate equivalent mitigation performance at significantly lower computational cost.

A scheme for compensation of nonlinear effects in multichannel data transfer systems based on dynamic neural networks is proposed. An improved quality of optical signal transfer in this scheme in comparison with the signal transfer in a scheme based on a neural network using symbols from only one channel is demonstrated.