Bi-Hamiltonian structure as a shadow of non-Noether symmetry

Abstract

In the present paper correspondence between non-Noether symmetries and bi-Hamiltonian structures is disscussed. We show that in regular Hamiltonian systems presence of the global bi-Hamiltonian structure is caused by symmetry of the space of solution. As an example well known bi-Hamiltonian realisation of Korteweg- De Vries equation is disscussed.