Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation.

We present a numerical study of solutions to the $2d$ focusing nonlinear Schr\"odinger equation in the exterior of a smooth, compact, strictly convex obstacle, with Dirichlet boundary conditions with cubic and quintic powers of nonlinearity. We study the effect of the obstacle on solutions traveling toward the obstacle at different angles and with different velocities. We introduce a concept of weak and strong interactions and show how the obstacle changes the overall behavior of solutions.