The deformation of phase space under small (*) perturbations to these systems is limited by the Kolmogorov-Arnold-Moser theorem.
One test for whether a system is of this type is if all movable singularities are poles. Given one of these systems, the Zakharov-Shabat construction finds operators L and M such that the time derivative of L equals the commutator of L and M, implying the spectrum of L is conserved. The Gelfand-Levitan-Marchenko equation can be used to solve those Lax equations in L and M for these systems via inverse scattering, giving rise to soliton solutions. The deformation of phase space under small (*) perturbations to these systems is limited by the Kolmogorov-Arnold-Moser theorem. In these systems, compact level sets of the invariants form tori, which locally have action-angle coordinates. Since the KdV equations have infinitely many symmetries, they describe this type of system. For 10 points, name these systems in which several independent conserved quantities allow for a closed-form solution.
One test for whether a system is of this type is if all movable singularities are poles.
integrable systems [accept Liouville integrable, completely integrable, or exactly solvable, prompt on solvable]