Soliton Shielding of the Focusing Nonlinear Schr?dinger Equation
Soliton Shielding of the Focusing Nonlinear Schr?dinger Equation
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DOI：
10.1103/physrevlett.130.127201
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发表时间：
2023-03-24
影响因子：
8.6
通讯作者：
Orsatti, Giuseppe
中科院分区：
文献类型：
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作者：
Bertola, Marco;Grava, Tamara;Orsatti, Giuseppe
我们首先考虑了有限N无限空间中聚焦非线性薛定谔(FNLS)方程的N个孤子的确定性气体，选择一个点谱在复谱平面的有界域上内插给定谱孤子密度。结果表明，当区域为圆盘且孤子密度为解析函数时，相应的确定性孤子气体出奇地产生以圆盘中心为点谱的单孤子解。我们称这种效应为孤子屏蔽。我们证明了这一行为是稳健的，并且对于随机孤子气体也是如此：实际上，当N孤子谱被选为随机变量时，无论是均匀分布在圆周上，还是根据Ginibre随机矩阵的本征值的统计来选择，孤子屏蔽现象都在极限N无穷大中持续存在。当区域为椭圆时，孤子屏蔽将光谱数据降低为集中在椭圆焦点之间的孤子密度。物理解是渐近阶跃振荡的，即初始轮廓是负x方向上的周期椭圆函数，而在负x方向上以指数形式快速消失。
We first consider a deterministic gas of N solitons for the focusing nonlinear Schrodinger (FNLS) equation in the limit N -infinity with a point spectrum chosen to interpolate a given spectral soliton density over a bounded domain of the complex spectral plane. We show that when the domain is a disk and the soliton density is an analytic function, then the corresponding deterministic soliton gas surprisingly yields the one-soliton solution with the point spectrum the center of the disk. We call this effect soliton shielding. We show that this behavior is robust and survives also for a stochastic soliton gas: indeed, when the N-soliton spectrum is chosen as random variables either uniformly distributed on the circle, or chosen according to the statistics of the eigenvalues of the Ginibre random matrix the phenomenon of soliton shielding persists in the limit N -infinity. When the domain is an ellipse, the soliton shielding reduces the spectral data to the soliton density concentrating between the foci of the ellipse. The physical solution is asymptotically steplike oscillatory, namely, the initial profile is a periodic elliptic function in the negative x direction while it vanishes exponentially fast in the opposite direction.