228 citations · 399 across the 17 of their papers we have counts for
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The Method of -Extension: The KdV Equation
Metin Gürses, Aslı Pekcan
In this work we generalize -extension that has been introduced recently. For illustration we use the KdV equation. We present five different -extensions…
Nonlocal KdV Equations
Metin Gürses, Aslı Pekcan
Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korte…
Discrete Symmetries and Nonlocal Reductions
Metin Gürses, Aslı Pekcan, Konstyantyn Zheltukhin
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
Nonlocal Hydrodynamic Type of Equations
Metin Gürses, Aslı Pekcan, Konstyantyn Zheltukhin
We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples.…
Superposition of the Coupled NLS and MKdV Systems
Metin Gürses, Aslı Pekcan
Superpositions of hierarchies of integrable equations are also integrable. The superposed equations, such as the Hirota equations in the AKNS hierarchy, cannot be considered as new…
-Dimensional Local and Nonlocal Reductions of the Negative AKNS System: Soliton Solutions
Metin Gürses, Aslı Pekcan
We first construct a -dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear…