Multi-place physics and multi-place nonlocal systems

被引:32
作者
Lou, S. Y. [1 ]
机构
[1] Ningbo Univ, Sch Phys Sci & Technol, Ningbo 315211, Zhejiang, Peoples R China
关键词
multi-place physics; multi-place nonlocal systems; symmetries; integrable systems; parity and time reversal; soliton theory; classical prohibitions; NONLINEAR SCHRODINGER-EQUATION; DE-VRIES EQUATION; ROGUE WAVES; SOLITON-SOLUTIONS; REVERSE SPACE; SHIFTED PARITY; KDV EQUATION; REDUCTIONS; INTEGRABILITY; DYNAMICS;
D O I
10.1088/1572-9494/ab770b
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
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页数:13
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