Dimer with gain and loss: Integrability and ${\mathcal{P}}{\mathcal{T}}$-symmetry restoration

A -symmetric nonlinear Schrödinger dimer is a two-site discrete nonlinear Schrödinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic -symmetric dimers are constructed as gain–loss extensions of their conservative, Hamiltonian, counterparts. We prove that all these damped-driven equations define completely integrable Hamiltonian systems. The second aim of our …