Solitons in \(\mathcal{PT}\)-symmetric systems with spin-orbit coupling and critical nonlinearity. (English) Zbl 07840925
In this paper, the authors establish a class of one-dimensional (1D) stable solitons in two-component \(\mathcal{PT}\)-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which models light propagation in a dual-core waveguide with skewed coupling between the cores are identified in the system’s parameter space. The authors determined the stability regions of the solitons in the system’s parameter space, and the main semi-infinite gap, and an additional finite annex gap. Also, stability boundaries are discovered by means of simulations of the perturbed evolution, which agree with results produced by the linear stability analysis for small perturbations. Moreover, distinct evolution scenarios are obtained for unstable solitons; stationary solitons are also found beyond the exceptional point, at which the \(\mathcal{PT}\) symmetry breaks down, interactions between adjacent solitons are explored too, featuring rebound or merger followed by blowup. Furthermore, slowly moving (tilted) solitons and fast ones develop different oscillations, and stability; the reduced diffractionless system, creates only unstable solitons. Some previous related results are improved and extended.
Reviewer: Xiaoming He (Beijing)
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 78A50 | Antennas, waveguides in optics and electromagnetic theory |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 35B20 | Perturbations in context of PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35C08 | Soliton solutions |
Keywords:
Townes solitons; quintic nonlinearity; spin-orbit interaction; dual-core waveguides; parity-time symmetryReferences:
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