Numerical study of the stability of the Peregrine breather

2015/07/24 by Christian Klein, Klein, C., Haragus, M. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1507.06766

openalex publication_date 2015/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Numerical study of the transverse stability of the Peregrine solution

Related

• Instability in nonlinear Schrödinger breathers
• Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations
• On the so-called rogue waves in the nonlinear Schrödinger equation
• Peregrine soliton as a limiting behavior of the Kuznetsov-Ma and Akhmediev breathers
• Amplification of wave groups in the forced nonlinear Schrödinger equation