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Numerical study of the transverse stability of the Peregrine solution

Abstract : We generalize a previously published numerical approach for the one‐dimensional (1D) nonlinear Schrödinger (NLS) equation based on a multidomain spectral method on the whole real line in two ways: first, a fully explicit fourth‐order method for the time integration, based on a splitting scheme and an implicit Runge‐Kutta method for the linear part, is presented. Second, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the 1D NLS equation and thus a y‐independent solution to the 2D NLS. It is shown that the Peregine solution is unstable agains all standard perturbations, and that some perturbations can even lead to a blow‐up for the elliptic NLS equation.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02570854
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 12 mai 2020 - 14:02:31
Dernière modification le : mercredi 13 mai 2020 - 01:35:33

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Christian Klein, Nikola Stoilov. Numerical study of the transverse stability of the Peregrine solution. Studies in Applied Mathematics, Wiley-Blackwell, 2020, ⟨10.1111/sapm.12306⟩. ⟨hal-02570854⟩

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