Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation

Equivalence group analysis is applied to the Kompaneets equation. We compute the equivalence Lie algebra for the corresponding generalized Kompaneets equation. We also show that the generalized Kompaneets equation is nonlinearly self-adjoint.
The principle of an a priori use of symmetries gives a possibility to use the equivalence algebra in order to approximate the Kompaneets equation by an equation having a wider class of symmetries. Using an additional symmetry of the approximating equation and the nonlinear self-adjointness, one can construct new group invariant solutions and conservation laws.