Tenth order solutions to the NLS equation with eighteen parameters

Pierre Gaillard (1) , Mickael Gastineau (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric as found for the lower orders.

Mots clés: NLS equation; wronskians; Peregrine breather; rogue waves

Domaines: Physique mathématique [math-ph]

Pierre Gaillard, Mickael Gastineau. Tenth order solutions to the NLS equation with eighteen parameters. 2015. ⟨hal-01165324⟩