182 citations · 981 across the 48 of their papers we have counts for
17 papers · 1 filter
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…
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…
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…
Traveling Wave Solutions of Degenerate Coupled Multi-KdV Equations
Metin Gürses, Aslı Pekcan
Traveling wave solutions of degenerate coupled -KdV equations are studied. Due to symmetry reduction these equations reduce to one ODE, where is a po…
2+1 KdV(N) Equations
Metin Gürses, Aslí Pekcan
We present some nonlinear partial differential equations in 2+1-dimensions derived from the KdV Equation and its symmetries. We show that all these equations have the same 3-solito…
Bi-presymplectic chains of co-rank one and related Liouville integrable systems
Maciej Błaszak, Metin Gürses, Kostyantyn Zheltukhin
Bi-presymplectic chains of one-forms of co-rank one are considered. The conditions in which such chains represent some Liouville integrable systems and the conditions in which ther…
On Non-Commutative Integrable Burgers Equations
M. Gurses, A. Karasu, R. Turhan
We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and…
Dynamical Systems and Poisson Structures
Metin Gurses, Gusein Sh. Guseinov, Kostyantyn Zheltukhin
We first consider the Hamiltonian formulation of systems in general and show that all dynamical systems in are bi-Hamiltonian. An algorithm is introduced to o…
Hydrodynamic type integrable equations on a segment and a half-line
Metin Gurses, Ismagil Habibullin, Kostyantyn Zheltukhin
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close…
Integrable discrete systems on R and related dispersionless systems
Maciej Blaszak, Metin Gurses, Burcu Silindir +1
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grai…
On a transformation between hierarchies of integrable equations
Metin Gurses, Kostyantyn Zheltukhin
A transforation between a hierarchy of integrable equations arising from the standard -matrix construction on the algebra of differential operators and a hierarchy of integrable…
Some Bi-Hamiltonian Equations in
Ahmet Ay, Metin Gurses, Kostyantyn Zheltukhin
Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and e…
Time Dependent Recursion Operators and Symmetries
Metin Gurses, Atalay Karasu, Refik Turhan
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of th…
Non-autonomous Svinolupov Jordan KdV Systems
Metin Gurses, Atalay Karasu, Refik Turhan
Non-autonomous Svinolupov-Jordan systems are considered. The integrability criteria of such systems are associated with the existence of recursion operators. A new non-autonomous K…
Recursion Operators of Some Equations of Hydrodynamic Type
M. Gurses, K. Zheltukhin
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2…