G. Chavchanidze

Bi-Hamiltonian Structure as a Shadow of Non-Noether Symmetry

The correspondence between non-Noether symmetries and bi-Hamiltonian structures is discussed. We show that in regular Hamiltonian systems the presence of the global bi-Hamiltonian structure is caused by the symmetry of the space of solution. As an example, the well-known bi-Hamiltonian realization of the Korteweg-de Vries equation is discussed.