An attempt to classification of the quasi rational solutions to the NLS equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These solutions can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t depending on 2N −2 parameters. It is remarkable to mention that in this representation, when all parameters are equal to 0, we recover the PN breathers.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. An attempt to classification of the quasi rational solutions to the NLS equation. 2015. ⟨hal-01231875v2⟩