These nonlinear structures of matter and the electromagnetic fields could appear as the attractors of a turbulent dynamics of a physical system that has been verified in direct numerical simulations of the dynamical problems.

In some cases (upper magnetosphere, tokamak plasma), when the kinetic effect of finite Larmor radius could be important, the pure kinetic approach can be used to get, from the first principles of the Poincare invariants conservation and the Liouville theorem, the final distributions of both nonuniform plasma and electromagnetic field at the transition layer. The demonstration of this approach is the main purpose of the presentation.