| Abstract |
We used the classical Lie symmetry method to investigate the damped Klein-Gordon equation with power-law non-linearity. We carried out a complete Lie symmetry classification by finding forms for arbitrary functions appearing in equation. This led to various cases. Corresponding to each case, we obtained one-dimensional optimal systems of subalgebras. Using these subalgebras, we reduced the non-linear Klein-Gordon equation to a set of ordinary differential equations and determined some invariant solutions. Additionally, we obtained conservation laws using the partial Lagrangian approach.
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