2015/07/24 by C. Klein, Christian Klein, Klein, C. +2 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Breather #Classical mechanics #Computer science #Constant (computer programming) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Instability #Mathematical analysis #Mathematics #Mechanics #Modulational instability #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Rogue wave #Stability (learning theory) #math.AP #nlin.SI
paper · pdf · doi:10.48550/arxiv.1507.06766
published in arXiv (Cornell University) (Cornell University)
arxiv created 2015/07/24 · openalex publication_date 2015/07/24 · arxiv updated 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solution to the nonlinear Schrödinger (NLS) equations. We first address the modulational instability of the constant modulus solution to NLS. Then we study numerically localized and nonlocalized perturbations of the Peregrine breather in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.