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

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.