Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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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, OktayWe 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.Article Citation - WoS: 1Citation - Scopus: 2Application of the Division Theorem To Nonlinear Physical Models for Constructing Traveling Waves(Politechnica University of Bucharest, 2013) Aslan, İsmailWe extend the so-called first integral method, which is based on the division theorem, to the Sharma-Tasso-Olver equation and the (2+1)-dimensional modified Boussinesq equation. Our approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Traveling wave solutions are constructed through the established first integrals.Article Citation - WoS: 10Citation - Scopus: 11Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations(Polish Academy of Sciences, 2013) Aslan, İsmailNonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.Article Citation - WoS: 32Citation - Scopus: 37Symbolic Computation and Construction of New Exact Traveling Wave Solutions To Fitzhugh-Nagumo and Klein-Gordon Equations(Walter de Gruyter GmbH, 2009) Öziş, Turgut; Aslan, İsmailWith the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, the so-called (G'/G)-expansion method, where the new and more general forms of solutions are also obtained. Periodic and solitary traveling wave solutions capable of moving in both directions are observed.