Journal of Basic and Applied Research International
 

Journal of Basic and Applied Research International, ISSN No. : 2395-3438 (Print), 2395-3446 (Online), Vol.: 21, Issue.: 3

Original Research Article

FAMILIES OF DEFORMATIONS OF THE THIRTEEN PEREGRINE BREATHER SOLUTIONS TO THE NLS EQUATION DEPENDING ON TWENTY FOUR PARAMETERS

 

PIERRE GAILLARD1* AND MICKAËL GASTINEAU2
1Université de Bourgogne, 9 Av. Alain Savary, Dijon, France.
2IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ Paris 06, Univ. Lille, 77 Av. Denfert-Rochereau, 75014 Paris, France.

Abstracts

We go on with the study of the solutions to the focusing one dimensional nonlinear Schrodinger equation (NLS). We construct here the thirteen's Peregrine breather (P13 breather) with its twenty four real parameters, creating deformation solutions to the NLS equation. New families of quasirational solutions to the NLS equation in terms of explicit ratios of polynomials of degree 182 in x and t multiplied by an exponential depending on t are obtained. We present characteristic patterns of the modulus of these solutions in the (x; t) plane, in function of the di erent parameters.

Keywords :

NLS equation; peregrine breather; rogue waves.