The beam control in two-channels PT-symmetric waveguide with fractional diffraction effect. (English) Zbl 1522.81102
Summary: The double gray solitons and beams control in two-channels PT-symmetric waveguide with fractional diffraction are studied. In the defocusing Kerr nonlinear effect, the stable double gray solitons can be obtained in the two-channels PT-symmetric waveguide. The effects of Lévy index and gain/loss coefficient on the existence, stability, gray scale and power of gray solitons are studied in detail. In addition, the transmission and control of bright soliton beams are studied in the two-channels PT-symmetric waveguide with focusing Kerr nonlinear effect. Due to the refractive index distribution of waveguide, the beam propagates as a respirator along the center when it inputs from the center. Otherwise, the propagation of beam occurs oscillation between two channels. The input positions and Lévy index can affect the frequency and amplitude of beam oscillation. And the gain/loss coefficient can cause energy flowing. Double beams can occur periodic elastic collisions and form a peak wave in the waveguide.
MSC:
| 81Q37 | Quantum dots, waveguides, ratchets, etc. |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 81Q93 | Quantum control |
| 81P47 | Quantum channels, fidelity |
| 70F05 | Two-body problems |
| 78A45 | Diffraction, scattering |
| 81U05 | \(2\)-body potential quantum scattering theory |
Keywords:
PT-symmetric waveguide; Kerr nonlinearity; fractional Schrödinger equation; gray soliton; beam controlReferences:
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