期刊
NONLINEAR DYNAMICS
卷 81, 期 1-2, 页码 353-371出版社
SPRINGER
DOI: 10.1007/s11071-015-1996-2
关键词
PT-symmetry; PT-reversibility; Schrodinger equation; Melnikov function; Perturbation; Chaos
资金
- PRIN-MURST Equazioni Differenziali Ordinarie e Applicazioni
- European Regional Development Fund [CZ.1.07/2.3.00/30.0005]
- [GACR P201/11/0768]
- [VEGA-MS 1/0071/14]
A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift-periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain-loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.
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