Integrable and Superintegrable Klein-Gordon and Schrödinger Type Dimers

A $PT$-symmetric dimer is a two-site nonlinear oscillator or a nonlinear Schrödinger dimer where one site loses and the other site gains energy at the same rate. We present a wide class of integrable oscillator type dimers whose Hamiltonian is of arbitrary even order. Further, we also present a wide class of integrable and superintegrable nonlinear Schrödinger type dimers where again the Hamiltonian is of arbitrary even order.

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