Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under -symmetric potentials
Reconstruction of stability for Gaussian spatial solitons in quintic–septimal nonlinear materials under -symmetric potentials
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发表时间：
2018
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通讯作者：
C. Dai;Yue-Yue Wang-Yue;Ding-Guo Yu
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作者：
C. Dai;Yue-Yue Wang-Yue;Ding-Guo Yu
在两种PT对称势下，给出了五阶七阶非线性介质中的常系数和变系数（2+1）维非线性薛定谔方程的高斯空间孤子解.利用线性稳定性分析和直接数值模拟相结合的方法研究了常系数方程解析解的稳定性。线性稳定性分析和直接数值模拟的结果具有高度的一致性，即常系数方程的高斯空间孤子的稳定情况只出现在离焦的五次非线性材料和聚焦的七次非线性材料中.在此基础上，通过选取合适的衍射形式β1（z），研究了基于有效传输距离Z（z）的变系数方程的稳定高斯空间孤子的重构问题。
Gaussian spatial soliton solutions of both the constant-coefficient andvariable-coefficient (2+1)dimensional nonlinear Schrödinger equations in quintic–septimal nonlinear materials with different diffractions are presented under two kinds of PT symmetric potentials. The linear stability analysis and direct numerical simulation are jointly utilized to investigate the stability for analytical solutions of the constant-coefficient equation. Results from the linear stability analysis and the direct numerical simulation possess a high degree of consistency, that is, the stable case for Gaussian spatial solitons of the constant-coefficient equation appears only in the defocusing quintic and focusing septimal nonlinear material. Moreover, reconstruction of stable Gaussian spatial solitons of the variable-coefficient equation is studied based on the expression of the effective propagation distance Z(z) by choosing an appropriate form of diffraction β1(z).