Solitons formed by ultrashort laser pulses propagating in a plasma

Using one-dimensional particle-in-cell simulations, authors observed the formation of solitons which can move with high group velocities when ultrashort laser pulses at a few cycles only propagate in underdense plasma near the critical density. There exist reflection and transmission when the solitons arrive at the plasma-vacuum boundary. When the intensity of initial laser pulses increases, the velocity of the formed solitons decreases. When a laser pulse at a few tens of cycles propagates in such a plasma, a cluster of solitons are left behind, and trapped in the plasma