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In this study, we model the dark matter and baryon matter distribution in theCosmic Web by means of highly nonlinear Schr\"{o}dinger type and reactiondiffusion wave mechanical descriptions. The construction of these wavemechanical models of the structure formation is achieved by introducing theFisher information measure and its comparison with a highly nonlinear termcalled the quantum potential in the wave equations. Strikingly, the comparisonof the nonlinear term and the Fisher information measure provides a dynamicaldistinction between lack of self-organization and self-organization in thedynamical evolution of the cosmic components. Mathematically equivalent to thestandard cosmic fluid equations, these approaches make it possible to followthe evolution of the matter distribution even into the highly nonlinear regimeby circumventing singularities. In addition, these wave formalisms are extendedto two-fluid descriptions of the coupled dark matter and baryon matterdistributions in the linear regime, in the Einstein de Sitter Universe (EdS) toconstruct toy models of the cosmic components in this relatively simpleUniverse model. Based on these two different wave mechanical formalisms, herefully analytical results for the dark matter and baryon distributions areprovided. Also, numerical realizations of the emerging weblike patterns arepresented from the nonlinear dynamics of the baryon component corresponding tosoliton-like solutions. These soliton-like solutions might represent a properdescription of filamentary structures even in the linear regime.

Connection between Fisher Information and Wave Mechanical Interpretations of Universe