Pashaev, Oktay
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Pashaev, O.
Pashaev, O. K.
Pashaev, Oktay K.
Pashaev, O. K.
Pashaev, Oktay K.
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oktaypashaev@iyte.edu.tr
pashaev@math.sinica.edu.tw
pashaev@vxjinr.jinr.ru
pashaev@math.sinica.edu.tw
pashaev@vxjinr.jinr.ru
Main Affiliation
04.02. Department of Mathematics
Status
Current Staff
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Documents
88
Citations
1099
h-index
18
Documents
96
Citations
1091
Scholarly Output
80
Articles
38
Views / Downloads
97753/42261
Supervised MSc Theses
15
Supervised PhD Theses
4
WoS Citation Count
638
Scopus Citation Count
661
Patents
0
Projects
3
WoS Citations per Publication
7.98
Scopus Citations per Publication
8.26
Open Access Source
71
Supervised Theses
19
| Journal | Count |
|---|---|
| Theoretical and Mathematical Physics | 10 |
| Journal of Physics A: Mathematical and Theoretical | 7 |
| Journal of Physics: Conference Series | 6 |
| Chaos, Solitons and Fractals | 5 |
| Springer Proceedings in Mathematics and Statistics | 4 |
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80 results
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Now showing 1 - 10 of 80
Article Citation - WoS: 15Citation - Scopus: 13Black Holes and Solitons of the Quantized Dispersionless Nls and Dnls Equations(Cambridge University Press, 2002) Pashaev, Oktay; Lee, Jyh HaoThe classical dynamics of non-relativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of the potential strength, recovers the standard Schrödinger equation. In addition, the classically forbidden region corresponds to the Planck constant analytically continued to pure imaginary, values. We apply the same procedure to the NLS and DNLS equations, constructing first the corresponding dispersionless limits and then adding quantum deformations. All these deformations admit the Lax representation as well as the Hirota bilinear form. In the classically forbidden region we find soliton resonances and black hole phenomena. For deformed DNLS the chiral solitons with single event horizon and resonance dynamics are constructed.Article Citation - WoS: 4Citation - Scopus: 4The Cauchy Problem for the Planar Spin-Liquid Model(IOP Publishing Ltd., 2005) Pashaev, Oktay; Chang, Nai-HengIn this paper, we study the Cauchy problem of a two-dimensional model for a moving ferromagnetic continuum and prove global existence and uniqueness of solutions. In addition, equivalence to the coupled system of nonlinear Schrödinger equations interacting with a Chern-Simons gauge field is established.Conference Object Citation - WoS: 24Citation - Scopus: 24Solitons of the Resonant Nonlinear Schrödinger Equation With Nontrivial Boundary Conditions: Hirota Bilinear Method(Pleiades Publishing, 2007) Lee, Jyh Hao; Pashaev, OktayWe use the Hirota bilinear approach to consider physically relevant soliton solutions of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions, recently proposed for describing uniaxial waves in a cold collisionless plasma. By the Madelung representation, the model transforms into the reaction-diffusion analogue of the nonlinear Schrödinger equation, for which we study the bilinear representation, the soliton solutions, and their mutual interactions.Master Thesis Resonance Solitons and Direct Methods in Soliton Theory(Izmir Institute of Technology, 2009) Duruk, Selin; Pashaev, Oktay; Pashaev, OktayThe Long-Short Wave interaction equations with adding quantum potential term and the Davey-Stewartson equation with addition of both, the quantum potential and the Hamiltonian terms are studied. These equations are reduced to different cases according to the choice of the quantum potential strength. For over critical case reductions to the non-linear diffusion-antidiffusion systems are derived. By the Hirota Direct Method one dissipaton solution of the system is derived. Two and three dissipaton (soliton) solutions are constructed explicitly. For special choice of the parameters they show the resonance character of interaction by fusion and fission of solitons.Conference Object Citation - WoS: 2Citation - Scopus: 2Self-Dual Chern-Simons Solitons and Quantum Potential(Taylor and Francis Ltd., 2001) Pashaev, Oktay; Lee, Jyh HaoAn influence of the quantum potential on the Chern-Simons solitons leads to quantization of the statistical parameter κ = me 2/g, and the quantum potential strength s = 1 - m 2. A new type of exponentially localized Chern-Simons solitons for the Bloch electrons near the hyperbolic energy band boundary are found.Conference Object Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States(Springer, 2024) Pashaev,O.K.We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define the complex potential, describing these quantum states by incompressible and irrotational classical hydrodynamic flow. In our approach, zeros of the wave function appear as a set of point vortices (sources) in plane with the same strength, allowing interpretation of them as images in a bounded domain. For the cat states we find fluid representation as descriptive of a point source in the oblique strip domain, with infinite number of periodically distributed images. For the annular domain, the infinite set of images is described by Jackson q-exponential functions. We show that these functions represent the wave functions of quantum coherent states of the q-deformed quantum oscillator in q-Fock-Bargmann representation and describe the infinite set of point vortices, distributed in geometric progression. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.Master Thesis Apollonius Representation and Complex Geometry of Entangled Qubit States(Izmir Institute of Technology, 2018) Parlakgörür, Tuğçe; Pashaev, OktayIn present thesis, a representation of one qubit state by points in complex plane is proposed, such that the computational basis corresponds to two fixed points at a finite distance in the plane. These points represent common symmetric states for the set of quantum states on Apollonius circles. It is shown that, the Shannon entropy of one qubit state depends on ratio of probabilities and is a constant along Apollonius circles. For two qubit state and for three qubit state in Apollonius representation, the concurrence for entanglement and the Cayley hyperdeterminant for tritanglement correspondingly, are constant along Apollonius circles. Similar results are obtained also for n- tangle hyperdeterminant with even number of qubit states. It turns out that, for arbitrary multiple qubit state in Apollonius representation, fidelity between symmetric qubit states is also constant along Apollonius circles. According to these, the Apollonius circles are interpreted as integral curves for entanglement characteristics. For generic two qubit state in Apollonius representation, we formulated the reflection principle relating concurrence of the state, with fidelity between symmetric states. The Möbius transformations, corresponding to universal quantum gates are derived and Apollonius representation for multi-qubit states is generated by circuits of quantum gates. The bipolar and the Cassini representations for qubit states are introduced, and their relations with qubit coherent states are established. We proposed the differential geometry for qubit states in Apollonius representation, defined by the metric on a surface in conformal coordinates, as square of the concurrence. The surfaces of the concurrence, as surfaces of revolution in Euclidean and Minkowski (Pseudo-Euclidean) spaces are constructed. It is shown that, curves on these surfaces with constant Gaussian curvature becomes Cassini curves. The hydrodynamic interpretation of integral curves for concurrence as a flow in the plane is given and the spin operators in multiqubit |PP...P states are discussed.Article Citation - WoS: 4Citation - Scopus: 4Power-Series Solution for the Two-Dimensional Inviscid Flow With a Vortex and Multiple Cylinders(Springer Verlag, 2009) Pashaev, Oktay; Yılmaz, OğuzThe problem of a point vortex and N fixed cylinders in a two-dimensional inviscid fluid is studied and an analytical-numerical solution in the form of an infinite power series for the velocity field is obtained using complex analysis. The velocity distribution for the case of two cylinders is compared with the existing results of the problem of a vortex in an annular region which is conformally mapped onto the exterior of two cylinders. Limiting cases of N cylinders and the vortex, being far away from each other are studied. In these cases, "the dipole approximation" or "the point-island approximation" is derived, and its region of validity is established by numerical tests. The velocity distribution for a geometry of four cylinders placed at the vertices of a square and a vortex is presented. The problem of vortex motion with N cylinders addressed in the paper attracted attention recently owing to its importance in many applications. However, existing solutions using Abelian function theory are sophisticated and the theory is not one of the standard techniques used by applied mathematicians and engineers. Moreover, in the N ≥ 3 cylinder problem, the infinite product involved in the presentation of the Schottky-Klein prime function must also be truncated. So, the approach used in the paper is simple and an alternative to existing methods. This is the main motivation for this study.Doctoral Thesis Enriched Finite Elements Method for Convevtion-Diffusion Problems(Izmir Institute of Technology, 2012) Şendur, Ali; Pashaev, OktayIn this thesis, we consider stabilization techniques for linear convection-diffusionreaction (CDR) problems. The survey begins with two stabilization techniques: streamline upwind Petrov-Galerkin method (SUPG) and Residual-free bubbles method (RFB). We briefly recall the general ideas behind them, trying to underline their potentials and limitations. Next, we propose a stabilization technique for one-dimensional CDR problems based on the RFB method and particularly designed to treat the most interesting case of small diffusion. We replace the RFB functions by their cheap, yet efficient approximations which retain the same qualitative behavior. The approximate bubbles are computed on a suitable sub-grid, the choice of whose nodes are critical and determined by minimizing the residual of a local problem. The resulting numerical method has similar stability features with the RFB method for the whole range of problem parameters. We also note that the location of the sub-grid nodes suggested by the strategy herein coincides with the one described by Brezzi and his coworkers. Next, the approach in one-dimensional case is extended to two-dimensional CDR problems. Based on the numerical experiences gained with this work, the pseudo RFBs retain the stability features of RFBs for the whole range of problem parameters. Finally, a numerical scheme for one-dimensional time-dependent CDR problem is studied. A numerical approximation with the Crank-Nicolson operator for time and a recent method suggested by Neslitürk and his coworkers for the space discretization is constructed. Numerical results confirm the good performance of the method.Master Thesis Exactly Solvab Q-Extended Nonlinear Classical and Quantum Models(Izmir Institute of Technology, 2011) Nalcı, Şengül; Pashaev, OktayIn the present thesis we study q-extended exactly solvable nonlinear classical and quantum models. In these models the derivative operator is replaced by q-derivative, in the form of finite difference dilatation operator. It requires introducing q-numbers instead of standard numbers, and q-calculus instead of standard calculus. We start with classical q-damped oscillator and q-difference heat equation. Exact solutions are constructed as q-Hermite and Kampe-de Feriet polynomials and Jackson q-exponential functions. By q-Cole-Hopf transformation we obtain q-nonlinear heat equation in the form of Burgers equation. IVP for this equation is solved in operator form and q-shock soliton solutions are found. Results are extended to linear q-Schrödinger equation and nonlinear q-Maddelung fluid. Motivated by physical applications, then we introduce the multiple q-calculus. In addition to non-symmetrical and symmetrical q-calculus it includes the new Fibonacci calculus, based on Binet-Fibonacci formula. We show that multiple q-calculus naturally appears in construction of Q-commutative q-binomial formula, generalizing all well-known formulas as Newton, Gauss, and noncommutative ones. As another application we study quantum two parametric deformations of harmonic oscillator and corresponding q-deformed quantum angular momentum. A new type of q-function of two variables is introduced as q-holomorphic function, satisfying q-Cauchy-Riemann equations. In spite of that q-holomorphic function is not analytic in the usual sense, it represents the so-called generalized analytic function. The q-traveling waves as solutions of q-wave equation are derived. To solve the q-BVP we introduce q-Bernoulli numbers, and their relation with zeros of q-Sine function.