Linearizable Second Order Monge]Amp`ere Equations

In this paper we consider the second order Monge]Amp`ere equations in 1q1., 2q1., and 3q1.dimensions. We face the problem of reducing to linear form the first order systems that are equivalent to the given Monge]Amp`ere equations. When the coefficients are assumed constant there are introduced invertible point transformations, suggested by the invariance with respect to one-parameter Lie groups of point symmetries, allowing us to get linear equations. Moreover, the case of nonconstant coefficients is discussed and some linearizable classes of Monge]Amp`ere equations with coefficients depending on first order derivatives are characterized.