Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations

Autor:	Calini, Annalisa, Schober, Constance M.
Rok vydání:	2018
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics 37K15 76B15
Druh dokumentu:	Working Paper
Popis:	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 Schr\"odinger 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. Comment: 12 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1803.06584 Zobrazit plný text záznamu View this record from Arxiv