Three nonlocal Alice-Bob sine-Gordon(ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton soluti...Three nonlocal Alice-Bob sine-Gordon(ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton solutions and three types of periodic solutions are presented. The multiple solutions, breather solution, double kink solution, and periodic solutions of the ABSG systems are obtained from the symmetry reductions of a coupled local sine-Gordon system.展开更多
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-plac...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.Multiplace 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 Schr?dinger(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.展开更多
基金the National Natural Science Foundation of China (Nos. 11435005, 11975131, 12235007)K.C.Wong Magna Fund in Ningbo University
文摘Three nonlocal Alice-Bob sine-Gordon(ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton solutions and three types of periodic solutions are presented. The multiple solutions, breather solution, double kink solution, and periodic solutions of the ABSG systems are obtained from the symmetry reductions of a coupled local sine-Gordon system.
基金sponsored by the National Natural Science Foundations of China(No.11975131,11435005)K C Wong Magna Fund in Ningbo University。
文摘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.Multiplace 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 Schr?dinger(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.
