The Hamilton-Jacobi Difference Equation

Nissim Elnatanov and Jeremy Schiff

Functional Differential Equations 3 279-286 (1996).

We study a system of difference equations which, like Hamilton's equations, preserves the standard symplectic structure on R2m. In particular, we construct a differential-difference equation which we call the Hamilton-Jacobi difference equation, the analog of the Hamilton-Jacobi equation for our discrete system. We solve the Hamilton-Jacobi difference equation in a simple case.