Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters.

Mots clés: Riemann theta functions; fredholm determinants; Wronskians; NLS equation; Peregrine breathers; Akhmediev's breathers; Rogue waves

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.. 2011. ⟨hal-00650528v1⟩