182 citations · 323 across the 27 of their papers we have counts for
30 papers
Comment on "Space-time shifted solitons and solution interactions for a generalized nonlocal nonlinear Schrödinger equation"
Aslı Pekcan
Zhou and Yu [Appl. Math. Lett. 178 (2026) 109937] studied the space-time shifted nonlocal nonlinear Schrödinger (NLS) equation $iq_t(x,t)=q_{xx}(x,t)-2σq^2(x,t) \bar{q}(x_0-x,t_0+λ…
Loop-type geometric folding of exact solutions of shifted nonlocal NLS and MKdV equations
Aslı Pekcan
Based on the notion of foldon, we introduce a geometric framework for constructing folded parametric wave representations of exact solutions of some shifted nonlocal nonlinear Schr…
Multi-place shifted nonlocal reductions of a multi-component AKNS system
Metin Gürses, Aslı Pekcan
Starting from a multi-component AKNS system, we obtain new shifted nonlocal nonlinear Schrödinger equations. We find 13 different shifted nonlocal nonlinear Schrödinger equations w…
Higher order Hirota bilinear forms
Metin Gürses, Aslı Pekcan
In this paper we study Hirota bilinear forms of the type . We prove that for the equations have three-soliton solutions if only if two o…
Shifted nonlocal reductions of 5-component Maccari system
Sena Baylı, Aslı Pekcan
In this work, we prove that shifted nonlocal reductions of integrable -dimensional -component Maccari system are particular cases of shifted scale transformations. We pre…
Method of -Extension via Frobenius Companion Matrices
Metin Gürses, Aslı Pekcan
Frobenius companion matrices arise when we write an -th order linear ordinary differential equation as a system of first order differential equations. These matrices and their t…
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…
On SK and KK Integrable Systems
Metin Gürses, Aslı Pekcan
To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other meth…
Moving null curves and integrability
Metin Gürses, Asli Pekcan
We study the null curves and their motion in a -dimensional flat space-time . We show that when the motion of null curves forms two surfaces in the integrability…
The Method of Hirota Bilinearization
Metin Gürses, Aslı Pekcan
Bilinearization of a given nonlinear partial differential equation is very important not only to find soliton solutions but also to obtain other solutions such as the complexitons,…
Multi-component AKNS systems
Metin Gürses, Aslı Pekcan
We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton so…
Soliton solutions of the shifted nonlocal NLS and MKdV equations
Metin Gürses, Aslı Pekcan
We find one- and two-soliton solutions of shifted nonlocal NLS and MKdV equations. We discuss the singular structures of these soliton solutions and present some of the graphs of t…
Local and nonlocal -dimensional Maccari systems and their soliton solutions
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In this work, by using the Hirota bilinear method, we obtain one- and two-soliton solutions of integrable -dimensional -component Maccari system which is used as a model…
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…
Hirota bilinear forms of the AKNS() systems
Metin Gürses, Aslı Pekcan
We study the AKNS() hierarchy for . We give the Hirota bilinear forms of these systems and present local and nonlocal reductions of them. We give the Hirota bilinear…
-dimensional AKNS() Systems:
Metin Gürses, Aslı Pekcan
In this work we continue to study negative AKNS() that is AKNS() system for . We obtain all possible local and nonlocal reductions of these equations. We construct th…
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…
Nonlocal Coupled HI-MKdV Systems
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We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of the…
-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…
Integrable Nonlocal Reductions
Metin Gürses, Aslı Pekcan
We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) a…
Nonlocal Modified KdV Equations and Their Soliton Solutions
Metin Gürses, Aslı Pekcan
We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the…
Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions
Metin Gürses, Aslı Pekcan
We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standa…