RMS width of pulses in nonlinear dispersive fibers: pulses of arbitrary initial form with chirp

We describe approximately the evolution of pulse parameters in nonlinear dispersive fibers and obtain a formula for the root mean square (rms) width of the pulses. The result is valid for frequency chirped initial pulses of arbitrary form propagating in very long fiber systems with weak normal dispersion. The derivation is based on a variational method for the nonlinear wave equation.