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14th Conference on "Recent Developments in Gravity", NEB-14; Ioannina; Greece; 8 June 2010 through 11 June 2010We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schrödinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation

Filamentary structures of the cosmic web and the nonlinear Schrödinger type equation