If we have a Jacobi PDE system with conservation law $\theta \in \Omega^1(M)$ such that $d \theta$ is non-degenerate 2-form , then we know this fact that it can be written as symplectic 2D 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 3D Symplectic Monge-Ampere equation arising from 3-forms ?

If we have a Jacobi PDE system with conservation law $\theta \in \Omega^1(M)$ such that $d \theta$ is non-degenerate 2-form , then we know this fact that it can be written as symplectic 2D 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 3D Symplectic Monge-Ampere equation arising from 3-forms ?

But automatically we have last three equations, because $h_i\in C^1$ so $\varphi\in C^2$ and by substituting these equations in first equation $A$ we get the generic 3D Monge-Ampere equation

But automatically we have last three equations, because $h_i\in C^1$ so $\varphi\in C^2$ and by substituting these equations in first equation $A$ we get the generic 3D Monge-Ampere equation.

But automatically we have last three equations, because $h_i\in C^1$ so $\varphi\in C^2$ and by substituting these equations in first equation $A$ we get the generic 3D Monge-Ampere equation