Conserved quantities for the non-linear Klein–Gordon equation

In this paper, the conserved quantities of the non-linear Klein–Gordon equation u_tt=u_xx+f(u) are derived. The Noether theorem is applied to the considered equation with an arbitrary function f(u) . Symmetry operators for all possible cases of the function f(u) are investigated. Then the conserved vectors are computed for each of these Noether symmetry operators.