Group classification of scalar fields with potential interaction

A system of scalar fields with Lagrangian L=(1/2)u_,iu^,i + V(u) in multi-dimensional space—time is considered. The structure of the permissible Lie group is studied for an arbitrary field multiplet. A complete group classification of field doublets and triplets is presented. All conservative fluxes of these systems are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 116–121, March, 1995.