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

I V Barashenkov; Mariagiovanna Gianfreda

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arXiv · 1405.3588

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

I V Barashenkov·Mariagiovanna Gianfreda

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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 $\mathcal{PT}$-symmetric nonlinear Schr\"odinger 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 $\mathcal{PT}$-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.

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BibTeX RIS

I V Barashenkov, Mariagiovanna Gianfreda. 2014-05-14. An exactly solvable $\mathcal{PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss. https://arxiv.org/abs/1405.3588

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