The solution of nonlinear Boltzmann equation with an external force

The method of Nikolskii is used for solving inhomogeneous Boltzmann equation in the presence of an arbitrary force, F(x,v,t). The necessary conditions that F(x,v,t) must satisfy for existence of Nikolskii transformation is derived. An exact analytical solution for spatially inhomogeneous Boltzmann equation is determined by resorting to the Nikolskii method.