Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation.
Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation.
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DOI：
10.1063/1.5123151
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发表时间：
2019-08
期刊：
影响因子：
2.9
通讯作者：
Jialiang Ji;Zong-Wei Xu;Zuo-nong Zhu
中科院分区：
文献类型：
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作者：
Jialiang Ji;Zong-Wei Xu;Zuo-nong Zhu
可积和不可积离散非线性薛定谔方程 (NLS) 是描述物理中许多现象的重要模型。最近，Ablowitz和Musslimani介绍了一类反空间、反时间和反时空非局部可积方程，包括非局部NLS方程、非局部正弦-Gordon方程、非局部Davey-Stewartson方程等。而且，可积非局部离散NLS已经通过逆散射变换精确求解。在本文中，我们研究了不可积离散非局部 NLS，它是反向空间非局部 NLS 的直接离散版本。通过应用离散傅立叶变换和改进的诺依曼迭代，我们以数值方式给出了其平稳解。检查平稳解的线性稳定性。最后，我们对非局部NLS方程的柯西问题进行了数值研究，发现其数值解与NLS方程的柯西问题的数值解相比有一些不同的、新的性质。
Integrable and nonintegrable discrete nonlinear Schrödinger equations (NLS) are significant models to describe many phenomena in physics. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time, and reverse space-time nonlocal integrable equations, including the nonlocal NLS equation, nonlocal sine-Gordon equation, nonlocal Davey-Stewartson equation, etc. Moreover, the integrable nonlocal discrete NLS has been exactly solved by inverse scattering transform. In this paper, we study a nonintegrable discrete nonlocal NLS, which is a direct discrete version of the reverse space nonlocal NLS. By applying discrete Fourier transform and modified Neumann iteration, we present its stationary solutions numerically. The linear stability of the stationary solutions is examined. Finally, we study the Cauchy problem for the nonlocal NLS equation numerically and find some different and new properties on the numerical solutions comparing with the numerical solutions of the Cauchy problem for the NLS equation.