scholarly journals Symmetries of the Hirota Difference Equation

2017 ◽  
Author(s):  
Andrei K. Pogrebkov ◽  
Keyword(s):  
Difference Equation ◽  
Hirota Difference Equation

scholarly journals Hirota Difference Equation and Darboux System: Mutual Symmetry

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 436 ◽  
Author(s):  
Andrei Pogrebkov
Keyword(s):  
Inverse Problems ◽  
Difference Equation ◽  
Discrete Symmetries ◽  
Integrable Equation ◽  
Direct And Inverse Problems ◽  
Independent Variables ◽  
Darboux System ◽  
Continuous Symmetries ◽  
Infinite Set ◽  
Hirota Difference Equation

We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R 3 . We demonstrated that specific properties of solutions of the HDE with respect to independent variables enabled introduction of an infinite set of discrete symmetries. We showed that degeneracy of the HDE with respect to parameters of these discrete symmetries led to the introduction of continuous symmetries by means of a specific limiting procedure. This enabled consideration of these symmetries on equal terms with the original HDE independent variables. In particular, the Darboux system appeared as an integrable equation where continuous symmetries of the HDE served as independent variables. We considered some cases of intermediate choice of independent variables, as well as the relation of these results with direct and inverse problems.

STABILITY AND BOUNDEDNESS PROPERTIES OF A RATIONAL EXPONENTIAL DIFFERENCE EQUATION

2020 ◽  
Vol 9 (7) ◽  
pp. 4945-4954
Author(s):  
J. Leo Amalraj ◽  
M. Maria Susai Manuel ◽  
D. S. Dilip ◽  
P. Venkata Mohan Reddy
Keyword(s):  
Difference Equation
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