Lie group classification a generalized coupled (2+1)-dimensional hyperbolic system

Abstract

In this paper we perform Lie group classification of a generalized coupled (2+1)-dimensional hyperbolic system, viz., $ u_{tt}-u_{xx}-u_{yy}+f(v) = 0,\,v_{tt}-v_{xx}-v_{yy}+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.