Effect of local Peregrine soliton emergence on statistics of random waves in the one-dimensional focusing nonlinear Schrödinger equation
Alexey Tikan
Abstract
The Peregrine soliton is often considered as a prototype of rogue waves. After recent advances in the semiclassical limit of the one-dimensional focusing nonlinear Schrödinger equation [M. Bertola and A. Tovbis, Commun. Pure Appl. Math. 66, 678 (2013)0010-364010.1002/cpa.21445] this conjecture can be seen from another perspective. In the present paper, connecting deterministic and statistical approaches, we numerically demonstrate the effect of the universal local emergence of Peregrine solitons on the evolution of statistical properties of random waves. Evidence of this effect is found in recent experimental studies in the contexts of fiber optics and hydrodynamics. The present approach can serve as a powerful tool for the description of the transient dynamics of random waves and provide new insights into the problem of the rogue waves formation.