On the contact linearization of Monge-Ampere equations

Abstract

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A Contact Linearization Problem for Monge-Ampère Equations and Laplace Invariants

“…Moreover dF ϑ ∧ dF η ∧ U ∧ dU = 0. Then there exists a local contact transformations that takes F ϑ and F η to q 1 and q 2 respectively and saves the point a (see [20]). In new coordinates λ = dq 1 ∧ dq 2 for some functions and the equation E ω has the following form:…”

“…hyperbolic or elliptic) Monge-Ampère equations and equations with constant coefficients was solved in [17]. The problem of contact equivalence Monge-Ampère equations to the wave equation v xx − v yy = 0 or the Laplace equation v xx + v yy = 0 was solved in [20].…”

On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients

“…Remark also that any equation which is equivalent to (12) belongs to the class H 1,1 (when k ≡ h ≡ 0) or H 2,2 (when k = 0 and h = 0). All equations of the class H 1,1 are locally equivalent to the wave equation v xy = 0 [26]. Therefore, we shall consider only equations of the class H 2,2 .…”

“…Equations of the class H 1,1 were considered in [26]. Any equation of the class H 2,2 is contact equivalent to an equation of the type [26] v…”

“…Later on Tunitskii took off this restriction and solved the problem for general equations [26]. The problem of classification of Monge-Ampère equations was also considered by Morimoto [25].…”