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Browsing by Author "Pashaev, Oktay"
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From qanalytic functions to double qanalytic Hermite binomials and qtraveling waves
Nalcı Tümer, Şengül; Pashaev, Oktay (IOP Publishing, 201610)We extend the concept of qanalytic function in two different directions. First we find expansion of qbinomial in terms of qHermite polynomials, analytic in two complex arguments. Based on this representation, we introduce ... 
Generalized GoldenFibonacci calculus and applications
Özvatan, Merve (Izmir Institute of Technology, 201807)In the present thesis the GoldenFibonacci calculus is developed and several applications of this calculus are obtained. The calculus is based on the Golden derivative as a finite difference operator with Golden and Silver ... 
Golden quantum oscillator and BinetFibonacci calculus
Pashaev, Oktay; Nalcı, Şengül (IOP Publishing, 201201)The Binet formula for Fibonacci numbers is treated as a qnumber and a qoperator with Golden ratio bases q = and Q = 1/, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for ... 
Hamiltonian dynamics of N vortices in concentric annular region
Pashaev, Oktay; Yılmaz, Oğuz (IOP Publishing, 201105)The problem of N vortex dynamics in annular domain is considered. The region is canonical one and allows by conformal mapping apply results to an arbitrary position of two cylinders in the plane. Using previous solution, ... 
The Hirota Method for reactiondiffusion equations with three distinct roots
Tanoğlu, Gamze; Pashaev, Oktay (AIP Publishing, 2004)The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reactiondiffusion equations of two types. The first equation has only nonlinear reaction part, while the second ... 
Integrable hierarchies and information measures
Parwani, Rajesh R.; Pashaev, Oktay (IOP Publishing, 200806)In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a onedimensional isentropic fluid, with ... 
Integrable vortex dynamics and complex Burgers' equation
Gürkan, Zeynep Nilhan (Izmir Institute of Technology, 2005)Integrable dynamical models of the point magnetic vortex interactions in the plane are studied. Reformulating the Euler equations for vorticity in the Helmholtz form, the Hamiltonian and Lax representations are found. ... 
Integrable vortex dynamics in anisotropic planar spin liquid model
Gürkan, Zeynep Nilhan; Pashaev, Oktay (Elsevier, 200810)The problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject ... 
Kaleidoscope of quantum coherent states and units of quantum information
Koçak, Aygül (Izmir Institute of Technology, 201807)In the present thesis, we study superposition of coherent states as the kaleidoscope of quantum coherent states, associated with regular npolygon symmetry and the roots of unity q2n = 1. These states are generalizations ... 
Madelung representation of damped parametric quantum oscillator and exactly solvable SchrödingerBurgers equations
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (American Institute of Physics Publishing, 20101201)We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrödinger equation with timedependent parameters. It allows us to find exact solutions of the ... 
On a 2+1dimensional WhithamBroerKaup system: A resonant NLS connection
Rogers, Colin; Pashaev, Oktay (WileyBlackwell, 201108)It is established that the WhithamBroerKaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1dimensional version of the WhithamBroerKaup system is ... 
Powerseries solution for the twodimensional inviscid flow with a vortex and multiple cylinders
Pashaev, Oktay; Yılmaz, Oğuz (Springer, 2009)The problem of a point vortex and N fixed cylinders in a twodimensional inviscid fluid is studied and an analyticalnumerical solution in the form of an infinite power series for the velocity field is obtained using complex ... 
Pseudo residualgree bubble functions for the stabilization of convectiondiffusionreaction prolems
Kaya, Adem (Izmir Institute of Technology, 2012)Convection  diffusion  reaction problems may contain thin regions in which the solution varies abruptly. The plain Galerkin method may not work for such problems on reasonable discretizations, producing nonphysical ... 
Qanalog of shock soliton solution
Nalcı, Şengül; Pashaev, Oktay (IOP Publishing, 201011)Based on Jackson's qexponential function, we introduce a qanalog of Hermite and Kampe de Feriet polynomials. It allows us to introduce and solve the qheat equation in terms of qKampe de Feriet polynomials with arbitrary ... 
Qanalytic functions, fractals and generalized analytic functions
Pashaev, Oktay; Nalcı, Şengül (IOP Publishing, 201401)We introduce a new class of complex functions of complex argument which we call qanalytic functions. These functions satisfy qCauchyRiemann equations and have real and imaginary parts as qharmonic functions. We show ... 
Qperiodicity, selfsimilarity and weierstrassmandelbrot function
Erkuş, Soner (Izmir Institute of Technology, 2012)In the present thesis we study selfsimilar objects by method's of the qcalculus. This calculus is based on qrescaled finite differences and introduces the qnumbers, the qderivative and the qintegral. Main object of ... 
QShock soliton evolution
Pashaev, Oktay; Nalcı, Şengül (Elsevier, 201209)By generating function based on Jackson's qexponential function and the standard exponential function, we introduce a new qanalogue of Hermite and Kampede Feriet polynomials. In contrast to qHermite polynomials with ... 
Quantum calculus of classical vortex images, integrable models and quantum states
Pashaev, Oktay (IOP Publishing, 201610)From two circle theorem described in terms of qperiodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular Nvortex polygon we find compact expression ... 
Relativistic DNLS and KaupNewell hierarchy
Pashaev, Oktay; Lee, Jyh Hao (Institute of Mathematics, 201707)By the recursion operator of the KaupNewell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit c → ∞ it reduces to DNLS equation and preserves ... 
Resonance solitons as black holes in Madelung fluid
Pashaev, Oktay; Lee, Jyh Hao (World Scientific Publishing, 200208)Envelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For ...