Direct perturbation theory for solitons of the derivative nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation.

A direct perturbation theory for solitons of the derivative nonlinear Schrödinger (DNLS) equation is developed based on a closure of eigenfunctions of the linearized DNLS equation around a one-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained. Under the known simple gaugelike transformation, these results are transformed into those for the perturbed modified nonlinear Schrödinger (MNLS) equation describing propagation of femtosecond pulses in optical fibers. A calculation of the perturbation-induced radiation fields for the perturbed DNLS and MNLS equations is also made. Our results for the perturbed MNLS equation can be reduced perfectly to those for the perturbed nonlinear Schrödinger equation in the small nonlinear-dispersion limit.