2018/03/17 by Annalisa Calini, Calini, Annalisa, Constance M. Schober +1
Mathematics · Physics and Astronomy · #37K15 #76B15 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:37K15 #msc:76B15 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1803.06584
12 pages, 4 figures
arxiv created 2018/03/17 · arxiv updated 2018/03/20
We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schrödinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.