| The long-time asymptotics of two colliding plane waves governed by the focusing nonlinear Schrodinger equation are analyzed via the inverse scattering method. The leading-order terms for the three resulting regions (the initial state with a phase perturbation, a transition state, and a residual state) are computed with error estimates using the steepest-descent method for Riemann-Hilbert problems. The non-decaying initial data requires a new adaptation of this method. It is found that at large times, the effect of the collision is felt in the initial state well beyond the shock front. |
