Multi-dimensional stable fundamental solitons and excitations in PT-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions
Multi-dimensional stable fundamental solitons and excitations in PT-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions
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DOI：
10.1016/j.cnsns.2017.09.014
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Yong Chen;Zhenya Yan
中科院分区：
文献类型：
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作者：
Yong Chen;Zhenya Yan
我们证明了具有无界增益和损耗分布的宇称-时间-（PT-）对称调和-高斯势在非均匀非线性介质中（如具有自聚焦和散焦情形的三次非线性薛定谔方程）可以支持全实线性谱、稳定的空间和时空孤子.精确的解析孤子在一维（1D）和更高的维（如，2D，3D）的几何形状，使他们被证明是稳定的，在给定的参数区域。特别地，可以发现几类数值基本孤子（特别是一维双峰孤子、二维涡旋孤子和三维双子弹孤子）在精确孤子的传播参数附近是稳定的。孤子的其他重要性质也进行了探讨，包括孤子的相互作用，稳定的孤子激发，和横向功率流。研究结果可为相应的理论分析和实验设计提供依据。
We demonstrate the parity-time-(PT-) symmetric harmonic-Gaussian potential with unbounded gain-and-loss distribution can support entirely-real linear spectra, stable spatial and spatio-temporal solitons in an inhomogeneous nonlinear medium (eg, cubic nonlinear Schrödinger equation with the self-focusing and defocusing cases). Exact analytical solitons are derived in both one-dimensional (1D) and higher-dimensional (eg, 2D, 3D) geometries such that they are verified to be stable in the given parameters regions. Particularly, several families of numerical fundamental solitons (especially the 1D double-peaked solitons, 2D vortex solitons, and 3D double bullets) can be found to be stable around the propagation parameters for exact solitons. Other significant properties of solitons are also explored including the interactions of solitons, stable soliton excitations, and transverse power flows. The results may excite the corresponding theoretical analysis and experiment designs.