Abstract
This paper studies a generalized Benney–Luke equation with time-dependent coefficients using Lie symmetry methods. Lie group classification with respect to the time-dependent coefficients is performed by first deriving the equivalence group of transformations. We obtain the principal Lie algebra consisting of two translation symmetries and then using the classifying relations along with the equivalence transformations we obtain six distinct cases of the time-dependent coefficients for which the principal Lie algebra extends. Symmetry reductions and group-invariant solutions are obtained for all these six cases. Finally, conservation laws are derived for two cases of the time-dependent coefficients by employing the multiplier method.
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