Work

Soliton synchronization with randomness: rogue waves and universality

Year: 2025

Type: article

Abstract: We consider an N -soliton solution of the focusing nonlinear Schrödinger equations. We give conditions for the synchronous collision of these N solitons. When the solitons velocities are well separated and the solitons have equal amplitude, we show that the local wave profile at the collision point scales as the sinc ( x ) function. We show that this behaviour persists when the amplitudes of the solitons are i.i.d. sub-exponential random variables. Namely the central collision peak exhibits universality : its spatial profile converges to the sinc ( x ) function, independently of the distribution. We derive Central Limit Theorems for the fluctuations of the profile in the near-field regime (near the collision point) and in the far-field regime.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae1435

Authors: Manuela Girotti, Tamara Grava, Robert Jenkins, Guido Mazzuca, Ken McLaughlin, Maxim Yattselev