Annals of Mathematical Sciences and Applications

Volume 2 (2017)

Number 2

Guest Editors: Tai-Chia Lin (National Taiwan University), Wen-Wei Lin (National Chiao Tung University), Tony Wen-Hann Sheu (National Taiwan University), Weichung Wang (National Taiwan University), Chih-wen Weng (National Chiao Tung University), and Salil Vadhan (Harvard University).

Numerical study of the stability of the Peregrine solution

Pages: 217 – 239

DOI: http://dx.doi.org/10.4310/AMSA.2017.v2.n2.a1

Authors

Christian Klein (Institut de Mathématiques de Bourgogne, Université de Bourgogne-Franche-Comté, Dijon, France)

Mariana Haragus (Laboratoire de Mathématiques de Besançon, Université de Bourgogne-Franche-Comté, Besançon, France)

Abstract

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.

Keywords

nonlinear Schrödinger equation, rogue waves, Peregrine solution

Full Text (PDF format)

Paper received on 3 May 2016.