Construction of Darboux coordinates and Poincaré–Birkhoff normal forms in noncanonical Hamiltonian systems

Darboux’s Theorem, Lie series and the standardization of the Salerno and Ablowitz–Ladik models

“…And in fact such a procedure can be exploited even in cases where the explicit form of the transformation is not known or does not exist in terms of elementary functions (see [16] for a related approach).…”