Abstract
We study the classification of invariant solutions of a class of nonlinear wave equations using Lie symmetry analysis and the underlying optimal systems of subalgebras. We propose a classification of Lie generators via optimal systems for four cases that arise therein. These optimal systems are presented in a convenient tree leaf diagram. Corresponding to each class, complete symmetry reductions and the invariant solutions are presented. To the best of our knowledge, this classification of optimal systems is new and do not appear in the literature. Our results also lead to the establishment of the local conservation laws corresponding to each conserved vector via the multiplier approach.
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