44 citations · 281 across the 35 of their papers we have counts for
38 papers
Generalized Hamiltonian formalism for spatially nonlocal nonlinear differential equations
Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov
In this work, we develop a generalized Hamiltonian formalism for spatially nonlocal field theories whose Lagrangian densities depend explicitly on both the local field and its spat…
Inverse scattering method for nonlinear negative first order coupled Klein-Gordon equation
Cihan Sabaz, Ilmar Gahramanov, Mansur I. Ismailov
The exact N-soliton solutions are derived for the coupled negative first order Klein-Gordon (CNKG) equation subject to vanishing boundary conditions by using the inverse scattering…
New Beta Integral from Supersymmetric Gauge Theory on Projective Space
Ilmar Gahramanov, Tuğba Hırlı, R. Semih Kanber +1
We derive a new beta-type basic hypergeometric integral identity from the equality of supersymmetric partition functions on . Unlike previously…
Erdal İnönü at 100: From the Sphere to the Plane
Ilmar Gahramanov
On the centennial of Erdal İnönü's birth, this article reflects on his scientific legacy and his role in shaping modern theoretical physics in Türkiye. We briefly discuss his life,…
Hamiltonian formulation of the supersymmetric KdV equation
Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov
We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical versi…
Lens Hyperbolic Modular Double
Yağmur Bülbül, Ilmar Gahramanov, Ali Mert Yetkin +1
We construct the lens hyperbolic modular double, a new algebraic structure whose intertwining operator produces a lens hyperbolic hypergeometric solution of the Yang--Baxter equati…
Bailey Pairs for the Tetrahedron Index
Ilmar Gahramanov, Sinan Ulaş Öztürk, Uveys Turhan
In this work, we develop new Bailey pairs for the pentagon identity satisfied by the tetrahedron index, expressible in terms of -series. Since the tetrahedron index underlies to…
Bailey chain approach to 2d dualities
Zehra Akbulut, Ilmar Gahramanov, Anıl Kahraman +2
We study a two-dimensional supersymmetric duality and construct novel Bailey pairs for the associated elliptic genera. This framework provides a systematic meth…
Ising 100: review of solutions
Oğuz Alp Ağırbaş, Anıl Ata, Eren Demirci +13
We present several known solutions to the two-dimensional Ising model. This review originated from the ``Ising 100'' seminar series held at Boğaziçi University, Istanbul, in 2024.
On Analytical Solutions in Witten's Cubic Open String Field Theory
Ilmar Gahramanov
This short review is based on the lecture given by the author at the Feza Gürsey Physics Days School 2024. Here we briefly review analytic solutions (in particular, the Erler-Schna…
Algebraic Structures Behind the Yang-Baxterization Process
Cansu Özdemir, Ilmar Gahramanov
We review the Yang-Baxterization process of braid group representations. We discuss the corresponding -CB algebras in the Yang-Baxterization process. We present diagrams of the…
Comments on flavor symmetry breaking and three-dimensional superconformal index
Ilmar Gahramanov
We investigate the superconformal index of a three-dimensional supersymmetric QCD with flavors. This theory confines with the breaking of a global…
Notes on the lens integral pentagon identity
H. Kübra Bag, Osman Ergec, Ilmar Gahramanov
We obtain the lens integral pentagon identity for three-dimensional mirror dual theories in terms of hyperbolic hypergeometric functions via reduction of equality for $\mathcal N=2…
On Bailey pairs for supersymmetric gauge theories on
Ilmar Gahramanov, Batuhan Keskin, Dilara Kosva +1
We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional …
The Gross-Pitaevskii equation from the Heisenberg spin chain
Osman Erkan Kaluc, Ilmar Gahramanov
In this paper, we revise the derivation of the Gross-Pitaevskii equation from the Heisenberg spin chain stressing physical aspects and all technicalities.
Hamiltonian formalism for nonlinear Schrödinger equations
Ali Pazarci, Umut Can Turhan, Nader Ghazanfari +1
We study the Hamiltonian formalism for second order and fourth order nonlinear Schrödinger equations. In the case of second order equation, we consider cubic and logarithmic nonlin…
Integrability from supersymmetric duality: a short review
Ilmar Gahramanov
Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In…
Variational symmetries of Lagrangian systems with higher-order derivatives
Ege Coban, Ilmar Gahramanov, Dilara Kosva
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples…
Bailey pairs for the q-hypergeometric integral pentagon identity
Ilmar Gahramanov, Osman Erkan Kaluc
In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality o…
Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
Erdal Catak, Ilmar Gahramanov, Mustafa Mullahasanoglu
We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superc…
Lens partition function, pentagon identity and star-triangle relation
Deniz N. Bozkurt, Ilmar Gahramanov, Mustafa Mullahasanoglu
We study the three-dimensional lens partition function for supersymmetric gauge dual theories on by using the gauge/YBE correspondence. This corre…
Gamma function solutions to the star-triangle equation
Ege Eren, Ilmar Gahramanov, Shahriyar Jafarzade +1
In the paper, we clarify some relations between solutions to the star-triangle equation via the gauge/YBE correspondence. We consider two solutions to the star-triangle relation in…
Pentagon identities arising in supersymmetric gauge theory computations
Deniz N. Bozkurt, Ilmar Gahramanov
The partition functions of three-dimensional N=2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition fun…
Integrable lattice spin models from supersymmetric dualities
Ilmar Gahramanov, Shahriyar Jafarzade
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mec…