Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Subject: search.filters.subject.Traveling wave solutionsWoS Q: search.filters.wosQuartile.Q2

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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.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 26
    Travelling Wave Solutions To Nonlinear Physical Models by Means of the First Integral Method
    (Springer Verlag, 2011) Aslan, İsmail
    This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully constructed for the equations considered. © Indian Academy of Sciences.