Semi-local one-dimensional optical wave turbulence

We study one-dimensional optical wave turbulence described by the 1D Schr{\"o}dinger-Helmholtz model for nonlinear light propagation in spatially nonlocal nonlinear optical media such as nematic liquid crystals. By exploiting the specific structure of the nonlocal response, we derive a reduced wave kinetic equation under a semi-local approximation that permits the study of weak-wave turbulent cascades. We explore the realisability of the wave turbulence predictions and demonstrate new turbulent behaviour related to spatial nonlocality. Moreover, we show strong dependence of the wave turbulence to the possible presence of incoherent solitonic structures.