In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

Self-similar solutions for fuzzy dark matter are very different from their counterparts in the standard cold model. In contrast to familiar hierarchical collapse of current model structure formation, they correspond an inverse blow-up. This fact highlights gravitational cooling process, which absence dissipation, allows system eject excess energy through intermittent expulsion clumps matter. Th...