Generation and propagation of subpicosecond pulse train

Higher-order nonlinear Schr"{o}dinger equation with the Hirotaconstraint conditions is considered, and an analytic solution, whichcan describe the modulational instability process, is presented.Based on the solution, a new pulse train without continuous wave (CW)background is generated in quadratures and the propagation of thepulse train is discussed in detail by simulating numerically. Theresults show that, unlike the propagation of the picosecond pulsetrain, under the effects of the higher-order terms, the pulse traincannot propagate along the fibre when the energy is very high;however, for some medium energy the pulse train can stably propagate.We also investigate the stability of the pulse train againstviolation of the Hirota conditions, and the results show that thepulse train can still propagate stably when the Hirota conditions arebroken.