Lie group classification: a generalised 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., 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.