An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Abstract

We show that a pair of coupled nonlinear oscillators, of which one oscillator has positive and the other one negative damping of equal rate, can form a Hamiltonian system.Small-amplitude oscillations in this system are governed by a PT -symmetric nonlinear Schrödinger dimer with linear and cubic coupling.The dimer also represents a Hamiltonian system and is found to be exactly solvable in elementary functions.We show that the nonlinearity softens the PT -symmetry breaking transition in the nonlinearly-coupled dimer: stable periodic and quasiperiodic states with large enough amplitudes persist for an arbitrarily large value of the gain-loss coefficient.