An integrable system is a dynamical system or system of differential equations with enough
compatible conserved structure to permit exact integration. The precise meaning depends
on the setting. A Hamiltonian system with 
degrees
of freedom is Liouville integrable when it has 
functionally independent integrals
of motion 
,
..., 
that are pairwise in involution,
 |
with respect to the Poisson bracket. For nonlinear partial differential equations, integrability commonly appears through a Lax pair, an inverse scattering method, an integrable hierarchy, or infinitely many conserved quantities.
