2014/05/14 by I V Barashenkov, Barashenkov, I V, Mariagiovanna Gianfreda +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #math-ph #math.MP #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.1405.3588
11 pages, 5 figures
arxiv created 2014/05/27 · arxiv updated 2014/05/28
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.