Solitons in large scale structures

I propose an alternative approach to extend the scope of the analytical understanding of structure formation in the universe. By assuming a scalar field ψ whose Lagrangian density implies a sine-Gordon equation for the unstable modes, we find the standard 1D solution for this equation over the nonlinear regime. The solutions predict the appearance of periodic nonlinear waves with soliton features in the cosmic fluid. I also introduce a procedure to transform ψ to the density matter field ρ and present some simple profiles of the resulting structures.