Zhong Ming, Chen Yong, Yan Zhenya, Tian Shou-Fu
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
Phys Rev E. 2022 Jan;105(1-1):014204. doi: 10.1103/PhysRevE.105.014204.
We introduce a class of physically intriguing PT-symmetric Dirac-δ-Scarf-II optical potentials. We find the parameter region making the corresponding non-Hermitian Hamiltonian admit the fully real spectra, and present the stable parameter domains for these obtained peakons, smooth solitons, and double-hump solitons in the self-focusing nonlinear Kerr media with PT-symmetric δ-Scarf-II potentials. In particular, the stable wave propagations are exhibited for the peakon solutions and double-hump solitons from some given parameters even if the corresponding parameters belong to the linear PT-phase broken region. Moreover, we also find the stable wave propagations of exact and numerical peakons and double-hump solitons in the interplay between the power-law nonlinearity and PT-symmetric potentials. Finally, we examine the interactions of the nonlinear modes with exotic waves, and the stable adiabatic excitations of peakons and double-hump solitons in the PT-symmetric Kerr nonlinear media. These results provide the theoretical basis for the design of related physical experiments and applications in PT-symmetric nonlinear optics, Bose-Einstein condensates, and other relevant physical fields.
我们引入了一类具有物理趣味性的PT对称狄拉克δ - 斯卡夫二世光学势。我们找到了使相应非厄米哈密顿量具有完全实谱的参数区域，并给出了在具有PT对称δ - 斯卡夫二世势的自聚焦非线性克尔介质中，这些得到的尖峰子、光滑孤子和双峰孤子的稳定参数域。特别地，即使相应参数属于线性PT相位破坏区域，对于某些给定参数的尖峰子解和双峰孤子也展示出了稳定的波传播。此外，我们还发现在幂律非线性与PT对称势相互作用中精确和数值尖峰子及双峰孤子的稳定波传播。最后，我们研究了非线性模式与奇异波的相互作用，以及PT对称克尔非线性介质中尖峰子和双峰孤子的稳定绝热激发。这些结果为PT对称非线性光学、玻色 - 爱因斯坦凝聚体及其他相关物理领域中相关物理实验的设计和应用提供了理论基础。
