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Hamiltonian formulation of the standard $\mathcal{PT}$-symmetric nonlinear Schrödinger dimer (1410.3581v1)
Published 14 Oct 2014 in nlin.SI, math-ph, and math.MP
Abstract: 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.