Twenty Two Parameter Deformations of the Twelfth Peregrine Breather Solutions to the NLS Equation
Pierre Gaillard *
Institut de Math´ematiques de Bourgogne, Universit ´e de Bourgogne, France
Mickael Gastineau
IMCCE, Observatoire de Paris, France
*Author to whom correspondence should be addressed.
Abstract
The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear
Schr¨odinger 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