Abstract
The most important property of the full group GE for applications is that it operates on the set of the solutions, that is, any solution of the equation E is transformed again into a solution of the same equation E. The study of this operation and its utilization for the construction of solutions is one of the main problems of the group analysis of differential equations. This chapter discusses the problem of group classification of differential equations E(θ), containing a so-called arbitrary element θ. It describes the formation of determining equations (DE). The determination of the full group GE of the given system of differential equations E is the first step in the group analysis of the system. The chapter describes the algorithm for the construction of the full group, and some of its peculiarities and properties have been noted. The aforementioned algorithm consists of three parts—forming the determining equations DE, constructing the space of solutions L of the equations DE, and generating the set Γ of the groups G1(ζ)—for all vector fields ζ Є L.
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