Dark solitons and their head-on collisions in nonlinear metamaterials

The evolution and collision of dark solitons appearing in nonlinear metamaterials are here considered using a Korteweg–de Vries description. A head-on collision between two dark solitons from opposite directions is investigated using the Poincaré–Lighthill–Kuo method. The phase shifts due to the collision are calculated explicitly. We provide computer experiment evidence about the change of trajectories and their phase shifts, in the space–time plot, corresponding upon collisions.