18 parameter deformations of the Peregrine breather of order 10 solutions of the NLS equation

We present here new solutions of the focusing one-dimensional nonlinear Schrödinger (NLS) equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric rings as found for the lower-orders.