Invariant solutions of integro-differential Vlasov–Maxwell equations in Lagrangian variables by Lie group analysis

The Lie point symmetries of the Vlasov–Maxwell system in Lagrangian variables are investigated by using a direct method for symmetry group analysis of integro-differential equations, with emphasis on solving nonlocal determining equations. All similarity reduction forms for the system are obtained by using different approaches and some analytical and numerical solutions are presented.