Traveling solitons in the parametrically driven nonlinear Schrodinger equation -: art. no. 016603

We show that the (undamped) parametrically driven nonlinear Schrodinger equation has wide classes of traveling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast.