Construction of alternative Hamiltonian structures for field equations (Q2766145)

This paper is devoted to the construction of Hamiltonian structures for systems of differential equations, without recourse to a Lagrangian which may be either unknown or may even fail to exist, starting from just the equation of motion. Here the authors use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures, for example: for heat, Burgers and potential Burgers equations. The authors improve on a previous version (of one of the authors) using recursion operators to increase the rank of the Poisson bracket matrices.