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Yayınlar
- MakaleAçık Erişim2018Scopus SJRQ3Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd–Bullough–Mikhailov equation
Ilhan, O.A.; Bulut, H.; Sulaiman, T.A.; Baskonus, H.M.
In this study, the modified exp (- Φ (η)) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov–Benjamin–Bona–Mahony–Burgers, one-dimensional Oskolkov equations and the Dodd–Bullough–Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.
AtıfScopus34OpenAlex35
İncele - MakaleAçık Erişim2018Scopus SJRQ3New structural dynamics of isolated waves via the coupled nonlinear Maccari’s system with complex structure
Ciancio, A.; Baskonus, H.M.; Sulaiman, T.A.; Bulut, H.
In this study, the modified exp (- ϕ(η)) -expansion function method is utilized in acquiring some new results to the coupled nonlinear Maccari’s system. The Maccari’s system is a nonlinear model that describes the dynamics of isolated waves, confined in a small part of space, in various fields such as hydrodynamic, plasma physics and nonlinear optics. We construct some new results with a complex structure to this model, such as; the trigonometric and hyperbolic function solutions. Under the suitable choice of the values of parameters, we plot the 2D, 3D and the contour graphs to some of the obtained solutions in this study. We observed that our results may be helpful in detecting the movement of an isolated wave in a small space to some practical physical problems.
AtıfScopus51OpenAlex53İncele - MakaleAçık Erişim2018Scopus SJRQ2Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation
Sulaiman, Tukur Abdulkadir; Aktürk, Tolga; Bulut, Hasan; Baskonus, Haci Mehmet
This study uses two mathematical approaches in constructing dark, bright, kink-type and singular soliton solutions to the Heisenberg ferromagnetic spin chain equation. The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation describes nonlinear dynamics of magnets. The acquired results in this study may help in explaining some physical meanings of some nonlinear physical models arising in electromagnetic waves. For instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic cotangent arises in the Langevin function for magnetic polarization. The 2-, 3-dimensional and the contour plots of all the acquired solutions are presented.
AtıfScopus72OpenAlex84İncele - MakaleAçık Erişim2018Scopus SJRQ1Numerical simulation and solutions of the two-component second order KdV evolutionarysystem
Yokus, Asif; Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan
In this study, with the aid of Wolfram Mathematica 11, the modified exp (−Ω(η)) -expansion function method is used in constructing some new analytical solutions with novel structure such as the trigonometric and hyperbolic function solutions to the well-known nonlinear evolutionary equation, namely; the two-component second order KdV evolutionary system. Second, the finite forward difference method is used in analyzing the numerical behavior of this equation. We consider equation (6.5) and (6.6) for the numerical analysis. We examine the stability of the two-component second order KdV evolutionary system with the finite forward difference method by using the Fourier-Von Neumann analysis. We check the accuracy of the finite forward difference method with the help of L2 and L∞ norm error. We present the comparison between the exact and numerical solutions of the two-component second order KdV evolutionary system obtained in this article which and support with graphics plot. We observed that the modified exp (−Ω(η)) -expansion function method is a powerful approach for finding abundant solutions to various nonlinear models and also finite forward difference method is efficient for examining numerical behavior of different nonlinear models.
AtıfScopus114WoS109OpenAlex139İncele - MakaleAçık Erişim2018Scopus SJRQ3Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules
Celik, E.; Bulut, H.; Baskonus, H.M.
In this manuscript, the modified exp (-Ω(ξ))-expansion function method is implemented to find the new solutions to the nonlinear differential equation being the transmission line model. We obtain some new solutions to this model such as complex, exponential, trigonometric and hyperbolic functions. We plot the two- and three-dimensional surfaces of each solutions obtained in this manuscript.
AtıfScopus7OpenAlex9İncele