Symmetry groups of the equations with nonlocal structure and an application for the collisionless Boltzmann equation

A generalized version of the direct methods of determination of symmetry group of the point transformations is presented for the equations with nonlocal structure. Also a new approach for solving of nonlocal determining equations is presented on the example of the collisionless Boltzmann equation. Symmetry group properties and similarity reduction forms of the collisonless Boltzmann equation are obtained and some mathematical and physical properties related to the equation based on reduction forms are discussed.