First-order nonlinear PDE ∂_t S + H(x, ∇S, t) = 0 for the action S. Characteristics coincide with Hamilton's equations; Crandall–Lions viscosity-solution theory handles non-smooth H.
Hamilton–Jacobi equation
Related concepts
- Partial differential equation (PDE)
- Method of characteristics
- Legendre transform (Lagrangian ↔ Hamiltonian)
- Noether 1918: continuous symmetry ⇒ conserved current
- Hamilton–Jacobi equation (classical mechanics)
- Beam dynamics
- Strong-field-approximation saddle-point: ∂_t S(p,t) = 0; Hamilton–Jacobi action
- φ⁴ scalar theory