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Traveling Waves of Ddes With Rational Nonlinearity
(Walter de Gruyter GmbH, 2016) Aslan, İsmail
It has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on the auxiliary equation method.
Citation - WoS: 32
Citation - Scopus: 37
Symbolic Computation and Construction of New Exact Traveling Wave Solutions To Fitzhugh-Nagumo and Klein-Gordon Equations
(Walter de Gruyter GmbH, 2009) Öziş, Turgut; Aslan, İsmail
With 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.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection