×

zbMATH — the first resource for mathematics

A geometrical approach to integrable systems admitting time dependent invariants. (English) Zbl 0736.35119
Topics in soliton theory and exactly solvable nonlinear equations, Proc. Conf. Nonlinear Evol. Equations, Solitons, Inverse Scattering Transform, Oberwolfach/Ger. 1986, 108-124 (1987).
Summary: [For the entire collection see Zbl 0721.00016.]
The structure of time dependent invariants for integrable systems is investigated. Using a purely geometrical framework a unified description of these quantities can be given. The crucial objects for the theory are master symmetries, i.e. vector fields giving rise to time dependent symmetries for the integrable system. It is shown how they fit into the algebraic structure, their close relationship to recursion operators and (bi-)Hamiltonian formulations is revealed. The results are very general, they can be applied to most of the known soliton systems as well as to finite dimensional examples.

MSC:
35Q58 Other completely integrable PDE (MSC2000)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)