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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation
Jia-Liang Ji1, Zong-Wei Xu2, Zuo-Nong Zhu3
1School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai 201620, People's Republic of China.
Abstract:
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.
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