Browsing by Author "Aslan, İsmail"
Now showing items 2140 of 46

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity
Aslan, İsmail (Elsevier, 20111114)We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G′/G)expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are ... 
Exact solutions for a local fractional DDE associated with a nonlinear transmission line
Aslan, İsmail (Institute of Physics Publishing, 20160901)Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differentialdifference equations. This study is devoted to a local fractional differentialdifference equation which ... 
Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform
Aslan, İsmail (Wiley, 201612)Dynamical behavior of many nonlinear systems can be described by fractionalorder equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact ... 
Exact solutions of a fractionaltype differentialdifference equation related to discrete MKdV equation
Aslan, İsmail (IOP Publishing, 201405)The extended simplest equation method is used to solve exactly a new differentialdifference equation of fractionaltype, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete ... 
The Expfunction approach to the Schwarzian Kortewegde Vries equation
Aslan, İsmail (Elsevier, 201004)By means of the Expfunction method and its generalization, we report further exact traveling wave solutions, in a concise form, to the Schwarzian Kortewegde Vries equation which admits physical significance in applications. ... 
The extended discrete (G′/G)expansion method and its application to the relativistic toda lattice system
Aslan, İsmail (American Institute of Physics Publising, 2009)We propose the extended discrete (G′/G)expansion method for directly solving nonlinear differentialdifference equations. For illustration, we choose the relativistic Toda lattice system. We derive further discrete hyperbolic ... 
The first integral method for constructing exact and explicit solutions to nonlinear evolution equations
Aslan, İsmail (Wiley, 201204)Problems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some ... 
Generalized solitary and periodic wave solutions to a (2 + 1)dimensional ZakharovKuznetsov equation
Aslan, İsmail (Elsevier, 201010)In this paper, the Expfunction method is employed to the ZakharovKuznetsov equation as a (2 + 1)dimensional model for nonlinear Rossby waves. The observation of solitary wave solutions and periodic wave solutions ... 
Multiwave and rational solutions for nonlinear evolution equations
Aslan, İsmail (De Gruyter, 201008)Nonlinear evolution equations always admit multisoliton and rational solutions. The Burgers equation is used as an example, and the expfunction method is used to eluciadte the solution procedure. 
A note on the (G′/G)expansion method again
Aslan, İsmail (Elsevier, 201009)We report an observation on two recent analytic methods; the (G′/G)expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved. 
On the application of the Expfunction method to nonlinear differentialdifference equations
Aslan, İsmail (Elsevier, 201206)When applying the Expfunction method to nonlineardifferential difference equations, Bekir (2010) [1] reported incorrect results. © 2012 Elsevier Inc. All rights reserved. 
On the application of the Expfunction method to the KP equation for Nsoliton solutions
Aslan, İsmail (Elsevier, 201211)We observe that the form of the KadomstevPetviashvili equation studied by Yu (2011) [S. Yu, Nsoliton solutions of the KP equation by Expfunction method, Appl. Math. Comput. (2011) doi:10.1016/j.amc.2010.12.095] is ... 
On the validity and reliability of the (G′/G)expansion method by using higherorder nonlinear equations
Aslan, İsmail; Öziş, Turgut (Elsevier, 200905)In this study, we demonstrate the validity and reliability of the socalled (G′/G)expansion method via symbolic computation. For illustrative examples, we choose the sixthorder Boussinesq equation and the ninthorder ... 
Rational and multiwave solutions to nonlinear evolution equations by means of the Expfunction method
Aslan, İsmail (Politechnica University of Bucharest, 2012)In this paper, we present a new application of the Expfunction method to carry out the integration of nonlinear evolution equations in terms of multiwave and rational solutions. To elucidate the solution procedure, we ... 
Rational and multiwave solutions to some nonlinear physical models
Aslan, İsmail (Romanian Academy, 2013)The Expfunction method is shown to be an effective tool to explicitly construct rational and multiwave solutions of completely integral nonlinear evolution equations. The procedure does not require the bilinear representation ... 
Remark on:"Expfunction method for the exact solutions of fifth order KdV equation and modified Burgers equation" [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009]
Aslan, İsmail (Elsevier, 201012)By means of the Expfunction method, Inan and Ugurlu [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009] reported eight expressions for being solutions to the two equations studied. In fact, all of them can be easily ... 
Similarity solutions to Burgers' equation in terms of special functions of mathematical physics
Öziş, Turgut; Aslan, İsmail (Jagellonian University, 201707)In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is ... 
Some exact and explicit solutions for nonlinear schrödinger equations
Aslan, İsmail (Polish Academy of Sciences Publishing House, 201301)Nonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödingertype equations in terms of traveling wave solutions. Through the ... 
Some exact and explicit solutions to a twocomponent, discrete, nonlinear Schrödinger model
Aslan, İsmail (National Research Council of Canada, 201108)Natural processes and phenomena often display discrete structure. The discrete nonlinear Schrödinger equations are used in both physics and biology to model periodic optical structures and energy transfer in proteins. In ... 
Some exact solutions for Toda type lattice differential equations using the improved (G′/G)expansion method
Aslan, İsmail (Wiley, 201203)Nonlinear lattice differential equations (also known as differentialdifference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables. ...