Yu Fajun
School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China.
Chaos. 2017 Feb;27(2):023108. doi: 10.1063/1.4975763.
Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.
从一个离散谱问题出发，我们推导出了一系列非线性离散方程，其中包括阿布洛维茨 - 拉迪克（AL）方程。我们对具有三个自由参数的AL方程的离散 rogue 波（DRW）解进行了分析研究。通过解析和数值方法得到了一阶和二阶DRW 轮廓的峰值和凹陷轨迹。特别地，我们研究了阿布洛维茨 - 穆斯利马尼方程在宇称 - 时间（PT）对称势中的色散解。并且我们考虑了非自治DRW解、参数控制及其与可变系数的相互作用，并预测了长寿命 rogue 波解。我们的结果可能为合成PT对称系统在非线性光学和凝聚态物理中的潜在应用提供有用信息。
