Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system

2017 ◽  
Vol 58 (10) ◽  
pp. 101514 ◽  
Author(s):  
Zhonglong Zhao ◽  
Bo Han
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Bäcklund Transformations ◽  
Lie Symmetry Analysis ◽  
Backlund Transformations

scholarly journals Lie Symmetry Analysis, Exact Solutions, Conservation Laws and Bäcklund Transformations of the Gibbons-Tsarev Equation

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1378
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
The Self ◽  
Bäcklund Transformations ◽  
Invariant Solutions ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Parameter Transformation ◽  
Backlund Transformations

In this paper, we mainly put the Lie symmetry analysis method on the Gibbons-Tsarev equation (GTe) to obtain some new results, including some Lie symmetries, one-parameter transformation groups, explicit invariant solutions in the form of power series. Subsequently, the self-adjointness of the GTe is singled out. It follows that the conservation laws associated with symmetries of GTe are constructed with the aid of Ibragimov’ method. Finally, we present the Bäcklund transformations so that more abundant solutions can be worked out.

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