Travelling solitons in the externally driven nonlinear Schr\"odinger equation

We consider the undamped nonlinear Schr\"odinger equation driven by a periodic external force. Classes of travelling solitons and multisoliton complexes are obtained by the numerical continuation in the parameter space. Two previously known stationary solitons and two newly found localised solutions are used as the starting points for the continuation. We show that there are two families of stable solitons: one family is stable for sufficiently low velocities while solitons from the second family stabilise when travelling faster than a certain critical speed. The stable solitons of the former family can also form stably travelling bound states.