Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Publisher: search.filters.publisher.IOP Publishing Ltd.Subject: search.filters.subject.Traveling wave solutions

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  • Article
    Citation - WoS: 11
    Citation - Scopus: 12
    Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types
    (IOP Publishing Ltd., 2016) Aslan, İsmail
    Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G′/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
  • Conference Object
    Citation - Scopus: 1
    From Q-Analytic Functions To Double Q-Analytic Hermite Binomials and Q-Traveling Waves
    (IOP Publishing Ltd., 2016) Nalcı Tümer, Şengül; Pashaev, Oktay
    We 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.