18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation

Pierre Gaillard () and Mickaël Gastineau ()
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Pierre Gaillard: Université de Bourgogne, 9 Av. Alain Savary, Dijon, France
Mickaël Gastineau: ASD, IMCCE-CNRS UMR8028, Observatoire de Paris, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 02, 1-14

Abstract: We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 inxandtby a product of an exponential depending ont. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.

Keywords: NLS equation; Wronskians; Peregrine breather; rogue waves; 35Q55; 37K10 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115500163

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