Chen Yong, Yan Zhenya, Mihalache Dumitru
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Chaos. 2019 Aug;29(8):083108. doi: 10.1063/1.5100294.
We discover that the physically interesting PT-symmetric Dirac delta-function potentials can not only make sure that the non-Hermitian Hamiltonians admit fully-real linear spectra but also support stable peakons (nonlinear modes) in the Kerr nonlinear Schrödinger equation. For a specific form of the delta-function PT-symmetric potentials, the nonlinear model investigated in this paper is exactly solvable. However, for a class of PT-symmetric signum-function double-well potentials, a novel type of exact flat-top bright solitons can exist stably within a broad range of potential parameters. Intriguingly, the flat-top solitons can be characterized by the finite-order differentiable waveforms and admit the novel features differing from the usual solitons. The excitation features and the direction of transverse power flow of flat-top bright solitons are also explored in detail. These results are useful for the related experimental designs and applications in nonlinear optics and other related fields.
我们发现，从物理角度来看有趣的PT对称狄拉克δ函数势不仅能确保非厄米哈密顿量具有完全实的线性谱，还能在克尔非线性薛定谔方程中支持稳定的尖峰子（非线性模式）。对于特定形式的δ函数PT对称势，本文所研究的非线性模型是精确可解的。然而，对于一类PT对称符号函数双阱势，一种新型的精确平顶亮孤子能在很宽的势参数范围内稳定存在。有趣的是，平顶孤子可由有限阶可微波形来表征，并具有与通常孤子不同的新颖特性。我们还详细探讨了平顶亮孤子的激发特性和横向功率流方向。这些结果对于非线性光学及其他相关领域的相关实验设计和应用很有用。
