New stationary distributions of the Vlasov–Maxwell–Fokker–Planck's system

In this paper we investigate the nonlinear Vlasov–Maxwell–Fokker–Plank (VMFP) system. We propose new families of distributions for the stationary VMFP equation, which is reduced to certain systems of nonlinear elliptic equations depending on arbitrary parameters. We consider the cases when these elliptic systems allow the reduction to the nonlinear PDEs of fourth order, or to the well-known Liouville equation.