Law of Large Numbers and Central Limit Theorem for random sets of
solitons of the focusing nonlinear Schr\"odinger equation
Law of Large Numbers and Central Limit Theorem for random sets of
solitons of the focusing nonlinear Schr\"odinger equation
We study a random configuration of $N$ soliton solutions $\psi_N(x,t;\boldsymbol{\lambda})$ of the cubic focusing Nonlinear Schr\"odinger (fNLS) equation in one space dimension. The $N$ soliton solutions are parametrized by a $N$-dimension complex vector $\boldsymbol{\lambda}$ whose entries are the eigenvalues of the Zakharov-Shabat linear spectral problem and by $N$ nonzero complex …