  Here, I derive an Ising Hamiltonian for $N$ coupled fibre-based Optical
Parametric Oscillators (OPOs). For this, I use the Lugiato-Lefever equation.
The derivation of the Hamiltonian does not pretend to be mathematically
correct, although it works under the assumption of plane waves propagating
through the OPOs. Its objective is rather to be as close as possible to the
Hamilton formalism than to be mathematically rigorous. The approach is based on
the assumptions that are justified from the physical point of view and are
implemented experimentally. The resulting Ising Hamiltonian contains all
necessary terms that are connected to the appearance and evolution of phase
solitons.
