Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object Citation - WoS: 5Citation - Scopus: 6Quantum Calculus of Classical Vortex Images, Integrable Models and Quantum States(IOP Publishing Ltd., 2016) Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyFrom two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.Conference Object Citation - Scopus: 1From Q-Analytic Functions To Double Q-Analytic Hermite Binomials and Q-Traveling Waves(IOP Publishing Ltd., 2016) Nalcı Tümer, Şengül; Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyWe extend the concept of q-analytic function in two different directions. First we find expansion of q-binomial in terms of q-Hermite polynomials, analytic in two complex arguments. Based on this representation, we introduce a new class of complex functions of two complex arguments, which we call the double q-analytic functions. As another direction, by the hyperbolic version of q-analytic functions we describe the q-analogue of traveling waves, which is not preserving the shape during evolution. The IVP for corresponding q-wave equation we solved in the q-D'Alembert form.