The Lie algebra of point symmetries of nonlocal collisionless Boltzmann equation in terms of moments

In this study we investigate Lie point symmetries of the collisionless Boltzmann equation in terms of the distribution and the moment functions, which is expressed in the system of the coupled nonlinear partial integro-differential equations. We consider the invariant criterion to analyze symmetry groups of equations with nonlocal form and then obtain Lie symmetries of the collisionless Boltzmann equation in terms of moments. Furthermore, the general similarity reduction forms by using the classification of the subgroups and the subalgebras of the system are discussed and exact invariant solutions are found.