lie point symmetry
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2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Mensah Folly-Gbetoula ◽  
Nkosingiphile Mnguni ◽  
A. H. Kara

A full Lie point symmetry analysis of rational difference equations is performed. Nontrivial symmetries are derived, and exact solutions using these symmetries are obtained.



Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1153
Author(s):  
Na Zhang ◽  
Guangyan Jia

In this paper, we introduce the Lie-point symmetry method into backward stochastic differential equation and forward–backward stochastic differential equations, and get the corresponding deterministic equations.





2018 ◽  
Vol 32 (27) ◽  
pp. 1850332
Author(s):  
Xiazhi Hao ◽  
Yinping Liu ◽  
Xiaoyan Tang ◽  
Zhibin Li ◽  
Wen-Xiu Ma

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.





2018 ◽  
Vol 11 (03) ◽  
pp. 1850040 ◽  
Author(s):  
A. H. Abdel Kader ◽  
M. S. Abdel Latif ◽  
F. El Bialy ◽  
A. Elsaid

In this paper, we obtained some new exact solutions of some nonlinear KdV-like equations using Lie point symmetry and [Formula: see text]-symmetry methods. The obtained solutions are in the form of doubly periodic, bright and dark soliton solutions.



2017 ◽  
Vol 72 (12) ◽  
pp. 1159-1171 ◽  
Author(s):  
Xia-Xia Du ◽  
Bo Tian ◽  
Jun Chai ◽  
Yan Sun ◽  
Yu-Qiang Yuan

AbstractIn this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton’s amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G′/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.





2017 ◽  
Vol 72 (9) ◽  
pp. 795-804 ◽  
Author(s):  
Quanyong Zhu ◽  
Jinxi Fei ◽  
Zhengyi Ma

AbstractThe nonlocal residual symmetry of a (2+1)-dimensional general Korteweg-de Vries (GKdV) system is derived by the truncated Painlevé analysis. The nonlocal residual symmetry is then localized to a Lie point symmetry by introducing auxiliary-dependent variables. By using Lie’s first theorem, the finite transformation is obtained for the localized residual symmetry. Furthermore, multiple Bäcklund transformations are also obtained from the Lie point symmetry approach via the localization of the linear superpositions of multiple residual symmetries. As a result, various localized structures, such as dromion lattice, multiple-soliton solutions, and interaction solutions can be obtained through it; and these localized structures are illustrated by graphs.



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