Collisions between spatiotemporal solitons of different dimensionality in a planar waveguide - art. no. 026604

A (2+1)-dimensional nonlinear Schrodinger equation including third-order di spersion is a natural model of a waveguide, in which strong temporal disper sion is induced by a grating in order to make the existence of two-dimensio nal spatiotemporal solitons possible. By means of analytical and numerical methods, we demonstrate that this model may support, simultaneously, stable dark quasi-one-dimensional (stripe) solitons and two-dimensional elevation solitons ("antidark solitons") in the form of weakly localized "lumps." Th e spatial position of lumps can be controlled by passing stripe dark solito ns through them in an arbitrary direction. To substantiate this mechanism, we analytically calculate a position shift generated by a headon collision between the stripe and lump. The obtained results are in good agreement wit h direct numerical simulations.