LIE SYMMETRIES AND INFINITE-DIMENSIONAL LIE-ALGEBRAS OF CERTAIN (1-DIMENSIONAL NONLINEAR EVOLUTION-EQUATIONS(1))

In this paper we discuss the Lie symmetries, symmetry algebra and simi larity reductions of two different equations introduced in the recent literature, namely, (i) a new coupled integrable dispersionless equati on and (ii) a new coupled hyperbolic variational equation. We point ou t that both the systems admit, in contradistinction to conventional Li e algebras in (1 + 1)-dimensional systems, infinite-dimensional Lie al gebras. Furthermore, we find physically interesting solutions for spec ial choices of the symmetry parameters.