Using the variational method, we derive simple, closed-form algebraic expressions that approximate the optimal input rms pulse width and the corresponding minimum output rms width for Gaussian pulses subject to both dispersive and nonlinear effects in single-mode fibers. We present results in both numerical and analytical forms and confirm them by the split-step Fourier numerical method. Our results cover both normal and anomalous dispersion in fibers with gain and loss. For the case of normal dispersion we show that both the optimal input and output widths are asymptotically linearly dependent on distance and dependent on the square roots f the dispersion coefficient and the transmitted power.
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