We show that under the replacement of time by a local in Lagrange equations, form equations is maintained if Lagrangian does not depend explicitly on time. also study corresponding modifications Hamilton and Hamilton--Jacobi equation.

The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour. PACS: 03.65-w, 03.65Pm, 03.65.-b

We give an example of the failure homogenization for a viscous Hamilton-Jacobi equation with non-convex Hamiltonian.

A close relationship between the classical HamiltonJacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholon...

A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators.

In this work, we consider the nonequilibrium thermodynamics of a reaction-diffusion system at a given temperature, using the Master equation. The information potential is defined as the logarithm of the stationary state. We compare the approximations, given by the Fokker–Planck equation and the Wentzel-Kramers-Brillouin method directly applied to the Master equation, and prove that they lead to...