If we have a Jacobi PDE system with conservation law $\theta \in \Omega^1(M)$ such that $d \theta$ is non-degenerate 2-form , we know this fact that it can be written as symplectic Monge-Ampere equation. so if we extend our Jacobi PDE system to 3-forms instead of 2-forms and assume conservation law $\theta \in \Omega^2(M)$ such that 3-form $d \theta$ is non-degenerate 3-form, then the new Jacobi PDE system can be written locally as the generalized Symplectic Monge-Ampere equation arising from 3-forms (generalized Monge-Ampere equation of 2-form to 3-form) ?