Victor LAHNO
Poltava State Pedagogical University,
2 Ostrogradskoho Str., Poltava, UKRAINE
E-mail: laggo@poltava.bank.gov.ua

Realizations of the conformal algebra and nonlinear invariant equations in three-dimensional space-time

Abstract:
We have constructed all inequivalent realizations of the Lie algebra of the conformal group c(1,2) by Lie vector fields in three independent and one dependent variables. We have also obtained new second-order partial differential equations in three-dimensional space-time invariant under the group c(1,2).