In this paper we perform Lie group classification of a generalized coupled (2+1)-dimensional hyperbolic system, viz., utt − uxx − uyy + f (v) = 0, vtt − vxx − vyy + g(u) = 0, which models many physical phenomena in nonlinear sciences. We show that the Lie group classification of the system provides us with an eleven-dimensional equivalence Lie algebra, whereas the principal Lie algebra is six-dimensional and has several possible extensions. It is further shown that several cases arise in classifying the arbitrary functions f and g, the forms of which include, amongst others, the power and exponential
functions. Finally, for three cases we carry out symmetry reductions for the coupled system

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