Wen Xiao-Yong, Yan Zhenya, Yang Yunqing
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China.
Chaos. 2016 Jun;26(6):063123. doi: 10.1063/1.4954767.
The integrable nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential [M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 110, 064105 (2013)] is investigated, which is an integrable extension of the standard nonlinear Schrödinger equation. Its novel higher-order rational solitons are found using the nonlocal version of the generalized perturbation (1,N-1)-fold Darboux transformation. These rational solitons illustrate abundant wave structures for the distinct choices of parameters (e.g., the strong and weak interactions of bright and dark rational solitons). Moreover, we also explore the dynamical behaviors of these higher-order rational solitons with some small noises on the basis of numerical simulations.
研究了具有自诱导宇称-时间对称势的可积非局部非线性薛定谔方程[M. J. 阿布洛维茨和Z. H. 穆斯利马尼，《物理评论快报》110, 064105 (2013)]，它是标准非线性薛定谔方程的可积扩展。利用广义微扰(1,N - 1)重达布变换的非局部形式找到了其新颖的高阶有理孤子。这些有理孤子展示了参数不同选择下丰富的波结构（例如，亮和暗有理孤子的强相互作用和弱相互作用）。此外，我们还基于数值模拟研究了这些高阶有理孤子在一些小噪声下的动力学行为。
