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Article Dans Une Revue Communications in Advanced Mathematical Sciences Année : 2019

Differential Relations for the Solutions to the NLS Equation and Their Different Representations

Résumé

Solutions to the focusing nonlinear Schr ̈odinger equation (NLS) of orderNdepending on 2N−2 real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasi-rational solutions to the NLS equation denoted by vN and have been explicitly constructed until order N=13. These solutions appear as deformations of the Peregrine breather PN as they can be obtained when all parameters are equal to 0. These quasi rational solutions can be expressed as a quotient of two polynomials of degree N(N+1 )in the variables x and t and the maximum of the modulus of the Peregrine breather of order N is equal to 2N+1. Here we give some relations between solutions to this equation. In particular, we present a connection between the modulus of these solutions and the denominator part of their rational expressions. Some relations between numerator and denominator of the Peregrine breather are presented.

Dates et versions

hal-02521648 , version 1 (27-03-2020)

Identifiants

Citer

Pierre Gaillard. Differential Relations for the Solutions to the NLS Equation and Their Different Representations. Communications in Advanced Mathematical Sciences, 2019, II (4), pp.235-243. ⟨10.33434/cams.558044⟩. ⟨hal-02521648⟩
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