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

摘要

The twelfth Peregrine breather ( P ₁₂ breather) solution to the focusing one dimensional nonlinear Schr?dinger 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.