Multicanonical analysis of rogue wave probabilities

• The multicanonical algorithm is found to predict accurately the probability of extremely rare rogue wave events.
• A simple parametrization for the rogue wave amplitude as a function of nonlinearity is presented.
• A rapid Runge–Kutta algorithm is developed for rogue wave propagation.

The multicanonical procedure is applied to the nonlinear Schrödinger equation in conjunction with a high order finite difference solution procedure to determine the probability distribution function (pdf) of rogue wave power and heights. The analysis demonstrates a logarithmic dependence of the slope of the pdf on the nonlinearity coefficient at large heights.