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Journal Articles Communications in Theoretical Physics Year : 2016

Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

Abstract

The Peregrine breather of order eleven (P11 breather) solution to the focusing one-dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P11 breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.
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Dates and versions

hal-01224526 , version 1 (04-11-2015)
hal-01224526 , version 2 (12-12-2015)

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Pierre Gaillard, Mickael Gastineau. Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather. Communications in Theoretical Physics, 2016, 65 (2), pp.136-144. ⟨10.1088/0253-6102/65/2/136⟩. ⟨hal-01224526v2⟩
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