Ten-parameter deformations of the sixth-order Peregrine breather solutions of the NLS equation

In this paper, we construct new deformations of the Peregrine breather of order 6 with ten real parameters. We obtain new families of quasi-rational solutions of the one-dimensional focusing nonlinear Schrödinger (NLS) equation. With this method, we construct new patterns of different types of rogue waves. We get, as already found for the lower order, the triangular configurations and rings isolated. Moreover, one sees for certain values of the parameters the appearance of new configurations of concentric rings. (paper)