  Configurational entropy (CE) consists of a family of entropic measures of
information used to describe the shape complexity of spatially-localized
functions with respect to a set of parameters. We obtain the Differential
Configurational Entropy (DCE) for similariton waves traveling in tapered
graded-index optical waveguides modeled by a generalized nonlinear
Schr\"odinger equation. It is found that for similariton's widths lying within
a certain range, DCE attains minimum saturation values as the nonlinear wave
evolves along the effective propagation variable $\zeta(t)$. In particular,
saturation is achieved earlier for lower values of the width, which we show
correspond to global minima of the DCE. Such low entropic values lead to
minimum dispersion of momentum modes as the similariton waves propagate along
tapered graded-index waveguides, and should be of importance in guiding their
design.
