Baskonus, H.M.; Sulaiman, T.A.; Bulut, H.

In this study, the extended sinh-Gordon equation expansion method is used in constructing various exact solitary wave solutions to the Klein–Gordon–Zakharov equations. The Klein–Gordon–Zakharov equations is a nonlinear model describing the interaction between the Langmuir wave and the ion acoustic wave in a high-frequency plasma. We successfully construct some topological, non-topological, compound topological and non-topological, singular, compound singular solitons and singular periodic wave solutions. Under the choice of suitable values of the parameters, the 2D, 3D and contour graphs to some of the reported solutions are also plotted.

AtıfScopus61·WoS58·OpenAlex67

İncele

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.

AtıfScopus83·OpenAlex108

İncele

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.

AtıfScopus34·OpenAlex35

İncele

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.

AtıfScopus51·OpenAlex53

İncele