Travelling solitons in the parametrically driven nonlinear Schroedinger   equation
  We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths nonpropogating and moving solitons co-exist while strongly forced solitons can only be stably when moving sufficiently fast. 
I.V.Barashenkov, E.V.Zemlyanaya, M.Baer