Differential Configurational Entropy in Nonlinear Self-Similar Optical Rogue Wave

Information theory plays an importantrole in the understanding of modern communication technology andcomputation. It has been used in many areas of research such aschemistry, biology, high-energy physics, computer science andcondensed matter physics. Differential Configuration entropy (DCE), theclassical counterpart of information theory, is a logarithmicmeasure of spatially-bounded functions in the Fourier space ofspatial complexity. It represents the exact measure of informationthat is needed to describe the spatial shape of functions withrespect to a set of parameters. We present the DCE for roguewaves travelling in the tapered graded index optical waveguidewhich is modelled by the inhomogeneous nonlinear Schr"odinger equation.It is found that there is a value of the rogue wave width for whichDCE has its minima, which correspond to a configuration of maximumcompressibility of information in the Fourier modes that describesthe spatial shape of the rogue. Lower the DCE, the wave solutionwill be more concentrated and the accuracy in predicting thelocalization of the wave will be higher. The DCE is obtained to theoptimal width of the rogue wave for which the informationstored in its spatial shape is most compressed into its momentummodes.