Eighth Peregrine breather solution of the NLS equation and multi-rogue waves

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

This is a continuation of a paper in which we present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work was based on a recent paper in which we had constructed a multi-parametric family of this equation in terms of wronskians. \\ Here we give a more compact formulation without limit. With this method, we construct Peregrine breather of order N=8 and multi-rogue waves associated by deformation of parameters.

Mots clés: Peregrine breathers; Riemann theta function; Fredholm determinant; NLS equation; Peregrine breathers.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Eighth Peregrine breather solution of the NLS equation and multi-rogue waves. 2012. ⟨hal-00664052v2⟩