Generation and propagation of pulse trains with ultrashort pulse separation

We investigate the nonlinear Schrödinger equation with variable coefficients by employing perturbation method. The analysis solution of the harmonic form is presented. The solution is one of forms to describe pulse trains with ultrashort pulse separation, which is about two orders of magnitude shorter than one of sech-type solitons considered before. And we could systematically adjust the perturbation parameter to obtain different pulse separation. As an example, we consider a nonlinear dispersive system with spatial parameter variations, and the results show that, the pulse train with ultrashort pulse separation presented by analysis solution may keep its shape even if the velocity is changed. The stability of the solution is discussed numerically, and the results reveal that the finite initial perturbations, such as white noise could not influence the main character of the solution. In addition, the stability of the solution is also discussed under more general conditions.