Linearizable Second Order Monge–Ampère Equations

AbstractIn this paper we consider the second order Monge–Ampère equations in (1+1), (2+1), and (3+1) dimensions. We face the problem of reducing to linear form the first order systems that are equivalent to the given Monge–Ampère 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–Ampère equations with coefficients depending on first order derivatives are characterized