Numerical study of the stability of the Peregrine solution

Christian Klein (1) , Mariana Haragus (2, 3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.

Mots clés: Nonlinear Schrödinger equation; Rogue waves; Peregrine solution

Domaines: Equations aux dérivées partielles [math.AP]

Christian Klein, Mariana Haragus. Numerical study of the stability of the Peregrine solution. Annals of Mathematical Sciences and Applications, 2017, 2 (2), pp.217-239. ⟨10.4310/AMSA.2017.v2.n2.a1⟩. ⟨hal-01674705⟩