Variational Poisson Structures

A variational Poisson structure on a differential equation \(\mathcal {E}\) is a \(\mathcal {C}\)-differential operator that takes cosymmetries of \(\mathcal {E}\) to its symmetries and possesses the necessary integrability properties. In the literature on integrable systems, Poisson structures are traditionally called Hamiltonian operators. We expose here the computational theory of local variational Poisson structures for normal equations. In this chapter the solutions of Problems 1.24, 1.25, 1.26, and 1.28 is presented.