The criteria for the formation of stationary pseudo-periodic structures in a system of gravitating particles, described by the Vlasov–Poisson system of equations. Conditions studied branching solutions of a nonlinear integral equation for a generalized gravitational potential, leading to the emergence of coherent complex states of relative equilibrium in non-stationary systems of massive particles.

Vlasov–Poisson equation, Newton–Gurzadyan potential, pseudo-periodicity of structures, Hammerstein equation

Mathematical modelling in actual problems of science and technics

Fimin Nikolay Nikolaevich,  ,  orcid.org/0000-0003-2629-5380,  KIAM RAS

Chechetkin Valery Mihailovich,  ,  orcid.org/0000-0002-5241-7962,  KIAM RAS