Deformations of the seventh order Peregrine breather solutions of the NLS equation with twelve parameters.

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We study the solutions of the one dimensional focusing NLS equation. Here we construct new deformations of the Peregrine breather of order 7 with 12 real parameters. We obtain new families of quasi-rational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We recover triangular configurations as well as rings isolated. As already seen in the previous studies, one sees appearing for certain values of the parameters, new configurations of concentric rings.

Mots clés: Akhmediev's solutions; NLS equation; Peregrine breathers; Akhmediev's solutions.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Deformations of the seventh order Peregrine breather solutions of the NLS equation with twelve parameters.. 2013. ⟨hal-00870156⟩