A Hamiltonian approach to the cohomogeneity one Ricci soliton equations and explicit examples of non-Kähler solitons

We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials and use this to find some explicit formulae for Ricci solitons not of Kähler type in five dimensions.