Travelling solitons in the externally driven nonlinear Schrödinger equation

Abstract

We consider the undamped nonlinear Schrödinger equation driven by a periodic external force. In the absence of damping, solitons do not have undulations on their tails; yet, we show that they can bind into stationary multisoliton complexes. Using two previously known stationary solitons and two newly found stationary complexes as starting points, we obtain classes of localized travelling waves by the numerical continuation in the parameter space. Two families of stable solitons are identified: one family is stable for sufficiently low velocities while solitons from the second family stabilize when travelling faster than a certain critical speed. The stable solitons of the former family can also form stably travelling bound states.