Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

This article is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and its deformations. Here we construct Peregrine breathers of order $N=9$ and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given.

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

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves. 2012. ⟨hal-00718003v2⟩