Soliton Synchronization with Randomness: Rogue Waves and Universality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917010424725504 |
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| author | Girotti, Manuela Grava, Tamara Jenkins, Robert Mazzuca, Guido McLaughlin, Ken Yattselev, Maxim |
| author_facet | Girotti, Manuela Grava, Tamara Jenkins, Robert Mazzuca, Guido McLaughlin, Ken Yattselev, Maxim |
| contents | 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 $\operatorname{sinc}(x)$ 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 $\operatorname{sinc}(x)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soliton Synchronization with Randomness: Rogue Waves and Universality Girotti, Manuela Grava, Tamara Jenkins, Robert Mazzuca, Guido McLaughlin, Ken Yattselev, Maxim Pattern Formation and Solitons Mathematical Physics Probability Exactly Solvable and Integrable Systems 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 $\operatorname{sinc}(x)$ 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 $\operatorname{sinc}(x)$ 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. |
| title | Soliton Synchronization with Randomness: Rogue Waves and Universality |
| topic | Pattern Formation and Solitons Mathematical Physics Probability Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2507.01253 |