Soliton Synchronization with Randomness: Rogue Waves and Universality

2025/07/02 by Manuela Girotti, Тамара Грава, Girotti, Manuela +9
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2507.01253

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-regime.

Citations

• General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation
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• Soliton Gas: Theory, Numerics and Experiments
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