  In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras,
similarity reductions and particular solutions of two different recently
introduced (2+1)-dimensional nonlinear evolution equations, namely (i)
(2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional
nonlinear Schr\"odinger type equation introduced by Zakharov and studied later
by Strachan. Interestingly our studies show that not all integrable higher
dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly
the two integrable systems mentioned above do not admit Virasoro type
subalgebras, eventhough the other integrable higher dimensional systems do
admit such algebras which we have also reviewed in the Appendix. Further, we
bring out physically interesting solutions for special choices of the symmetry
parameters in both the systems.
