Nonlocal symmetry and exact solutions of the (2+1)-dimensional modified Bogoyavlenskii–Schiff equation

2016 ◽  
Vol 25 (6) ◽  
pp. 060201 ◽  
Author(s):  
Li-Li Huang ◽  
Yong Chen
Keyword(s):  
Exact Solutions ◽  
Nonlocal Symmetry

Nonlocal symmetries and the nth finite symmetry transformation or AKNS system

2018 ◽  
Vol 32 (27) ◽  
pp. 1850332
Author(s):  
Xiazhi Hao ◽  
Yinping Liu ◽  
Xiaoyan Tang ◽  
Zhibin Li ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Symmetry Transformation ◽  
Original System ◽  
Point Symmetry ◽  
Auxiliary Variables ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Akns System ◽  
Lie Point Symmetry ◽  
Physical Phenomena

In this paper, by introduction of pseudopotentials, the nonlocal symmetry is obtained for the Ablowitz–Kaup–Newell–Segur system, which is used to describe many physical phenomena in different applications. Together with some auxiliary variables, this kind of nonlocal symmetry can be localized to Lie point symmetry and the corresponding once finite symmetry transformation is calculated for both the original system and the prolonged system. Furthermore, the nth finite symmetry transformation represented in terms of determinant and exact solutions are derived.

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