Optical control of spatial Riemann waves and Burgers’ equation dynamics

Simple Riemann waves (RWs), solutions of the Inviscid Burgers’ Equation (IBE), are of fundamental importance to study shock formation in different physical frameworks beyond hydrodynamics [1]. Recently, RW signatures in time domain have been reported in the context of nonlinear optical fibres [2-4]. Nevertheless, only limited control was demonstrated on the propagation of these peculiar optical pulses [5]. Here, we describe a method to control the nonlinear dynamics of their spatial counterpart, i.e., Riemann beams (RBs). Such RBs can be theoretically generated with arbitrary trajectories, by properly engineering an external potential and the application of an initial phase profile on the beam.