  We study the class of 3-dimensional nonlinear 2-hessian equations mentioned
in the text. We perform preliminary group classification on 2-hessian equation.
In fact, we find additional equivalence transformation on the space
(x,y,z,u,f), with the aid of a method, then we take their projections on the
space (x,y,z,f), so we prove an optimal system of one-dimensional Lie sub
algebras of this equation is generated by A1 to A12, which introduced in
theorem 2, ultimately, A number of new interesting nonlinear invariant models
are obtained which have non-trivial in variance algebras. The result of these
works is a wide class of equations which summarized in table. So at the end of
this work, some exact solutions of 2-hessian equation are presented. The paper
is one of the few applications of an algebraic approach to the group
classification using Lie method.
