Article Contents
Article Contents

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

• * Corresponding author: Ben Muatjetjeja
• 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.

Mathematics Subject Classification: 35J47, 35J61.

 Citation:

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