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Multi-place physics and multi-place nonlocal systems
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2020-04-22 , DOI: 10.1088/1572-9494/ab770b
S Y Lou

Multi-place nonlocal systems have attracted attention from many scientists. In this paper, we mainly review the recent progresses on two-place nonlocal systems (Alice-Bob systems) and four-place nonlocal models. Multi-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity, time reversal, charge conjugates, rotations, field reversal and exchange transformations. Multi-place nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry reductions. On the other hand, to solve multi-place nonlocal systems, one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group, such that the separated systems are coupled local ones. By using the separation method, all the known powerful methods used in local systems can be applied to nonlocal cases. In this review article, we take two-place and four-place nonlocal nonlinear Schrodinger (NLS) systems and Kadomtsev-Petviashvili (KP) equations as simple examples to explain how to derive and solve them. Some types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.

中文翻译:

多地点物理和多地点非局部系统

多地点非局部系统引起了许多科学家的关注。在本文中,我们主要回顾了两地非局部系统(Alice-Bob 系统)和四地非局部模型的最新进展。多地点系统首先可以通过使用具有离散对称群的多重缩放方法从许多物理问题中推导出来,包括奇偶校验、时间反转、电荷共轭、旋转、场反转和交换变换。多位置非局部系统也可以通过离散对称约简从耦合非线性系统的对称约简中推导出来。另一方面,为了解决多处非局部系统,可以使用与合适的离散对称群相关的对称-反对称分离方法,使得分离的系统是耦合的局部系统。通过使用分离方法,本地系统中使用的所有已知的强大方法都可以应用于非本地情况。在这篇综述文章中,我们以二位和四位非局部非线性薛定谔 (NLS) 系统和 Kadomtsev-Petviashvili (KP) 方程为例来解释如何推导和求解它们。特别强调了与非局部系统相关的某些类型的新物理和数学点。
更新日期:2020-04-22
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