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Browsing by Author "Pashaev, Oktay"
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Abelian ChernSimons vortices and holomorphic Burgers hierarchy
Pashaev, Oktay; Gürkan, Zeynep Nilhan (Springer, 200707)We consider the Abelian ChernSimons gauge field theory in 2+1 dimensions and its relation to the holomorphic Burgers hierarchy. We show that the relation between the complex potential and the complex gauge field as in ... 
Algebraic methods and exact solutions of quantum parametric oscillators
Çetindaş, Osman (Izmir Institute of Technology, 201906)In this thesis, we study different approaches for solving the Schrödinger equation for quantum parametric oscillators. The WeiNorman algebraic approach, the Lewis Riesenfeld invariant approach, the MalkinMankoTrifonov ... 
Apollonius representation and complex geometry of entangled qubit states
Parlakgörür, Tuğçe (Izmir Institute of Technology, 201807)In 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 ... 
Bianchi I model: An alternative way to model the presentday Universe
Russell, Esra; Kılınç, Can Battal; Pashaev, Oktay (Oxford University Press, 201408)Although the new era of highprecision cosmology of the cosmic microwave background (CMB) radiation improves our knowledge to understand the infant as well as the presentday Universe, it also leads us to question the main ... 
Black holes and solitons of the quantized dispersionless NLS and DNLS equations
Pashaev, Oktay; Lee, Jyh Hao (Cambridge University Press, 200207)The classical dynamics of nonrelativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of ... 
The Cauchy problem for the planar spinliquid model
Pashaev, Oktay; Chang, NaiHeng (IOP Publishing, 2005)In this paper, we study the Cauchy problem of a twodimensional model for a moving ferromagnetic continuum and prove global existence and uniqueness of solutions. In addition, equivalence to the coupled system of nonlinear ... 
Chiral resonant solitons in ChernSimons theory and BroerKaup type new hydrodynamic systems
Lee, Jyh Hao; Pashaev, Oktay (Elsevier, 201208)New BroerKaup type systems of hydrodynamic equations are derived from the derivative reactiondiffusion systems arising in SL(2, R) KaupNewell hierarchy, represented in the nonMadelung hydrodynamic form. A relation with ... 
Classical and Quantum Euler equation
Eti, Neslihan (Izmir Institute of Technology, 2007)In the present thesis we give generalization of analytical mechanics to describe dynamical systems with dissipation. The Lagrangian function in this case is determined by nonstationary pseudoRiemannian metric for the ... 
Damped parametric oscillator and exactly solvable complex Burgers equations
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (IOP Publishing, 2012)We obtain exact solutions of a parametric Madelung fluid model with dissipation which is linearazible in the form of Schrödinger equation with time variable coefficients. The corresponding complex Burgers equation is solved ... 
Damping oscillatory models in general theory of relativity
Tığrak Ulaş, Esra (Izmir Institute of Technology, 2007)In my thesis we have studied the universe models as dynamical systems which can be represented by harmonic oscillators. For example, a harmonic oscillatior equation is constructed by the transformation of the Riccati ... 
Degenerate fourvirtualsoliton resonance for the KPII
Pashaev, Oktay; Francisco, Meltem L. Y. (Springer, 200507)We propose a method for solving the (2+1)dimensional Kadomtsev Petviashvili equation with negative dispersion (KPII) using the second and third members of the disipative version of the AKNS hierarchy. We show that ... 
Dissipative hierarchies and resonance solitons for KPII and MKPII
Francisco, Meltem L. Y.; Lee, Jyh Hao; Pashaev, Oktay (Elsevier, 200703)We show that dissipative solitons (dissipatons) of the second and the third members of SL(2,R) AKNS hierarchy give rise to the real solitons of KPII, while for SL(2,R) KaupNewell hierarchy they give solitons of MKPII. ... 
Energy localization in maximally entangled two and threequbit phase space
Pashaev, Oktay; Gürkan, Zeynep Nilhan (IOP Publishing, 201206)Motivated by theMobius transformation for symmetric points under the generalized circle in the complex plane, the system of symmetric spin coherent states corresponding to antipodal qubit states is introduced. In terms of ... 
Enriched finite elements method for convevtiondiffusionreaction problems
Şendur, Ali (Izmir Institute of Technology, 2012)In this thesis, we consider stabilization techniques for linear convectiondiffusionreaction (CDR) problems. The survey begins with two stabilization techniques: streamline upwind PetrovGalerkin method (SUPG) and Residualfree ... 
Entanglemend and topological soliton structures in Heisenberg spin models
Gürkan, Zeynep Nilhan (Izmir Institute of Technology, 2010)Quantum entanglement and topological soliton characteristics of spin models are studied. By identifying spin states with qubits as a unit of quantum information, quantum information characteristic as entanglement is ... 
Entanglement in two qubit magnetic models with dm antisymmetric anisotropic exchange interaction
Gürkan, Zeynep Nilhan; Pashaev, Oktay (World Scientific Publishing, 201003)In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the DzialoshinskiiMoriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model ... 
Envelope soliton resonances and broerkauptype nonmadelung fluids
Pashaev, Oktay (Springer, 201208)We derive an extended nonlinear dispersion for envelope soliton equations and also find generalized equations of the nonlinear Schrödinger (NLS) type associated with this dispersion. We show that space dilatations imply ... 
Exact solutions of forced Burgers equations with time variable coefficients
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (Elsevier, 201307)In this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ̇(t)/μ(t))U+UUx=(1/2μ(t))Uxxω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a ... 
Exactly solvab qextended nonlinear classical and quantum models
Nalcı, Şengül (Izmir Institute of Technology, 2011)In the present thesis we study qextended exactly solvable nonlinear classical and quantum models. In these models the derivative operator is replaced by qderivative, in the form of finite difference dilatation operator. ... 
Exactly solvable Madelung fluid and complex Burgers equations: A quantum SturmLiouville connection
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (Springer, 201211)Quantum SturmLiouville problems introduced in our paper (Büyükaşi{dotless}k et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, ...