Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein–Gordon equations

Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class (1+1)-dimensional generalized nonlinear Klein-Gordon equations is first-order prolongation its point groupoid, and then carry out complete group classification this class. Since it normalized, algebraic method naturally applied here. Using specific structure class, essentially employ classical Lie theorem on realizations algebras by vector fields line. This approach allows us to enhance previous results symmetries from substantially simplify proof. After finding number integer characteristics cases Lie-symmetry extensions are invariant under action study, exhaustively describe successive within