Hamiltonian formulation of the standard $\mathcal{PT}$-symmetric   nonlinear Schr\"odinger dimer
  The standard $\mathcal{PT}$-symmetric dimer is a linearly-coupled two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. We show that despite gain and loss, the standard $\mathcal{PT}$-dimer is a Hamiltonian system. We also produce a Lagrangian formulation for the dimer. 
I. V. Barashenkov
nlin.SI math-ph math.MP