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Browsing Mathematics / Matematik 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 ... 
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 ... 
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 ... 
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 ... 
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 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, ... 
Exactly solvable quantum SturmLiouville problems
Atılgan Büyükaşık, Şirin; Pashaev, Oktay; Tığrak Ulaş, Esra (American Institute of Physics Publising, 2009)The harmonic oscillator with timedependent parameters covers a broad spectrum of physical problems from quantum transport, quantum optics, and quantum information to cosmology. Several methods have been developed to ... 
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 ... 
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 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 ...