Phase manifold geometry of burgers hierarchy

Geometry of the Recursion Operators for the GMV System

“…If we assume some spectral properties, as doubly degenerate eigenspaces this theory allows to extend to field theories the classical Liouville theorem for the complete integrability of Hamiltonian dynamics, see [8,9,28,31]. Relaxing the conditions on the eigenspaces, the ideas behind Liouville integrability can be extended even to dissipative dynamics, [7]. There is a nice picture of the relation of the P-N structures on the manifold of potentials for the GZS system in canonical gauge, the manifold of potentials for the same system in pole gauge and the manifold of the corresponding Jost solutions, see [12,Chap.…”

Noncommutative integrability and recursion operators

“…Integrability of dissipative dynamics can be put in the same setting by assuming [10] different spectral hypothesis for the tensor field T . The last formulation has the advantage of being more appropriate to deal with dynamics with infinitely many degrees of freedom (completely integrable field theories).…”

Symplectic Structures and Quantum Mechanics

“…In terms of such an operator the classical Liouville theorem on the integrability can be extended also to the infinite dimensional case. The same operator can be used to deal with Burgers equation 10 . Some years ago it was suggested 11 the use of complex canonical coordinates in the formulation of a generalized dynamics including classical and quantum mechanics as special cases.…”