Chen Yong, Yan Zhenya, Mihalache Dumitru, Malomed Boris A
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, 100190, China.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
Sci Rep. 2017 Apr 28;7(1):1257. doi: 10.1038/s41598-017-01401-3.
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
自从宇称-时间-（[公式：见原文]）对称量子力学被提出以来，一些具有[公式：见原文]对称势的线性和非线性模型的基本性质已得到研究。然而，先前对[公式：见原文]对称波的研究局限于周围介质中恒定的衍射系数。在此，我们研究了具有广义[公式：见原文]对称斯卡夫-II势的非线性介质中可变衍射系数对光束动力学的影响。随着衍射参数的增加，破坏的线性[公式：见原文]对称相可能会恢复。发现一维和二维孤子的连续族是稳定的。特别地，解析地找到了一些稳定孤子。确定了孤子的存在范围和传播动力学。还研究了通过绝热改变参数对孤子的变换以及孤子之间的碰撞。我们还探讨了在一个结合了可变衍射系数和具有全局平衡增益与损耗的复势的模型中恒定强度波的演化，该模型比[公式：见原文]对称模型更具一般性，但具有相似的性质。我们的结果可能为非线性非均匀光学介质中[公式：见原文]对称非线性波的新实验提供建议。
