# Time Evolution of Optical Rogue Waves (Rogons) in the Causal Interpretation of Quantum Mechanics

Time Evolution of Optical Rogue Waves (Rogons) in the Causal Interpretation of Quantum Mechanics

In this Demonstration, modified Peregrine solitons resembling optical rogue waves (here called rogons) are studied in the causal interpretation of L. de Broglie and D. Bohm. The rogons have a variable function and a variable initial position (for the first case). The word rogon has its origin in physical similarities between the rogue waves and solitary wave. If the waves reappear virtually unaffected in size or shape shortly after their interactions, Yan [1, 3] called them "rogons".

The causal interpretation (also called hidden variables theory, ontological interpretation, de Broglie–Bohm theory, pilot-wave theory or Bohmian mechanics) has the feature that particles are regarded as both particles and waves, where the wave in the configuration space affects the motion of the particle. The trajectories could be interpreted as streamlines of a certain kind of fluid. The complex-valued wave obeys the nonlinear Schrödinger equation and the guiding equation (velocity) of the particles is derived by the continuity equation.

The graphic on the left shows the density (blue), the quantum potential (red), and the velocity (green). On the right, you can see the density and the trajectories in -space. The velocity and the quantum potential are scaled to fit.

(x,t)