Higher order Peregrine breathers and multi-rogue waves solutions of the NLS equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

This work is a continuation of a recent paper in which we have constructed a multi-parametric family of solutions of the focusing NLS equation given in terms of wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of quasi-rational solutions. Here we construct Peregrine breathers of orders N=4, 5, 6 and the multi-rogue waves corresponding in the frame of the NLS model first explained by Matveev et al. in 2010. In the cases N=4, 5, 6 we get convenient formulas to study the deformation of higher Peregrine breather of order 4, 5 and 6 to the multi-rogue waves via variation of the free parameters of our construction.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Higher order Peregrine breathers and multi-rogue waves solutions of the NLS equation. 2012. ⟨hal-00589556v3⟩