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Advances in Research, ISSN: 2348-0394,Vol.: 7, Issue.: 2


Twenty Two Parameter Deformations of the Twelfth Peregrine Breather Solutions to the NLS Equation


Pierre Gaillard1* and Mickaël Gastineau2
1Institut de Mathématiques de Bourgogne, Université de Bourgogne, France.
2IMCCE, Observatoire de Paris, France.

Article Information
(1) Shi-Hai Dong, Professor of Department of Physics, School of Physics and Mathematics National Polytechnic Institute, Building 9, Unit Professional Adolfo Lopez Mateos, Mexico.
(1) Suma Debsarma, University of Calcutta, India.
(2) Andrej Kon’kov, Moscow Lomonosov State University, Russia.
Complete Peer review History: http://sciencedomain.org/review-history/14350


The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation in terms of explicit quotients of polynomials of degree 156 in x and t by a product of an exponential depending on t are obtained. The patterns of the modulus of these solutions in the (x; t) plane, in function of the different parameters are studied in details.

Keywords :

NLS equation; wronskians; Peregrine breather; rogue waves.

Full Article - PDF    Page 1-11

DOI : 10.9734/AIR/2016/25636

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