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- MakaleAçık Erişim2021Scopus SJRQ3New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method
Dusunceli, Faruk; Celik, Ercan; Askin, Muzaffer; Bulut, Hasan
In this study, the doubly dispersive equation is presented by the application of the improved Bernoulli sub-equation function method (IBSEFM). The doubly dispersive equation which is a nonlinear partial differential equation is transformed into nonlinear ordinary differential equation using a wave transformation and then is solved by IBSEFM. Some new solutions are successfully constructed. All the obtained solutions in this study have been satisfied the doubly dispersive equation. In the present study, we have used Wolfram Mathematica 9 software for all of the computations and graphic plottings.
AtıfScopus41OpenAlex48
İncele - MakaleAçık Erişim2019Scopus SJRQ3On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering
Sulaiman, T.A.; Bulut, H.; Yokus, A.; Baskonus, H.M.
The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this study, we investigate the coupled Boussinesq equation which arises in the shallow water waves for two-layered fluid flow. The modified exp (- φ(ζ)) -expansion function method is utilized in reaching the solutions to this equation such as the topological kink-type soliton and singular soliton solutions. The interesting 2D and 3D graphics of the obtained analytical solutions in this study are presented. Via one of the reported analytical solutions, the finite forward difference method is used in obtaining the approximate numerical and exact solutions to this equation. The Fourier–Von Neumann analysis is used in checking the stability of the used numerical method with the studied model. The L 2 and L ∞ error norms are computed. We finally present a comprehensive conclusion to this study.
AtıfScopus83OpenAlex108İncele - 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.
AtıfScopus34OpenAlex35İncele - 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