标题： 孤立子同步与随机性：异常波与普遍性 显示英文标题

标题： Soliton Synchronization with Randomness: Rogue Waves and Universality

摘要： 我们考虑聚焦非线性薛定谔方程的$N$孤子解。 我们给出这些$N$孤子同步碰撞的条件。 当孤子的速度充分分离且孤子具有相等振幅时，我们表明碰撞点处的局部波形按$\operatorname{sinc}(x)$函数进行缩放。 我们证明当孤子的振幅是独立同分布的次指数随机变量时，这种行为仍然存在。 即中心碰撞峰表现出普适性：其空间轮廓收敛到$\operatorname{sinc}(x)$函数，与分布无关。 我们推导了近场区域（靠近碰撞点）和远场区域中轮廓波动的中心极限定理。 显示英文摘要

摘要： We consider an $N$-soliton solution of the focusing nonlinear Schr\"{o}dinger 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.