  The dynamical behavior resulting from an initial discontinuity in focusing
media is investigated using a combination of numerical simulations and Whitham
modulation theory for the focusing nonlinear Schrodinger equation. Initial
conditions with a jump in either or both the amplitude and the local wavenumber
are considered. It is shown analytically and numerically that the space-time
plane divides into expanding domains in which the solution is described by a
slow modulation of genus-zero, genus-one or genus-two solutions, their precise
arrangement depending on the specifics of the initial datum
