Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet; Akturk, Tolga

This study acquires the wave solutions of the two well-known nonlinear models, namely; the modified Benjamin–Bona–Mahony and the coupled Klein–Gordon equations. The modified Benjamin–Bona–Mahony is a nonlinear model that describes the long surface gravity waves of small amplitude and the coupled Klein–Gordon equation describes the quantized version of the relativistic energy–momentum relation. We successfully acquire some new solutions to these models such as kink-type and soliton solutions in complex hyperbolic functions form. We plot the 3D and 2D surface of the all the obtained solutions in this study. The mathematical approach used in this study is the sine-Gordon expansion method.

AtıfScopus33·OpenAlex40

İncele

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.

AtıfScopus73·OpenAlex76

İncele

Bulut, Hasan; Isik, Hilal Arslanoglu; Sulaiman, Tukur Abdulkadir; Atangana, A; Bulut, H; Hammouch, Z; Baskonus, HM; Mekkaoui, T; Belgacem, FB

The improved Bernoulli sub-equation function method is used in extracting some new exponential function solutions to the (2+1)-dimensional Broer-Kaup-Kupershmidt system. It is of vital effort to look for more solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt system, which are very helpful for coastal and civil engineers to apply the nonlinear water models in a harbor and coastal design. All the obtained solutions satisfied the (2+1)-dimensional Broer-Kaup-Kupershmidt system. The two-and three-dimensional shapes of all the obtained solutions in this paper are also presented. All the computations and the graphics plots in this study are carried out with the aid of the Wolfram Mathematica 9.

AtıfWoS29·OpenAlex31

İncele

Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet; Yazgan, Tugba

In this study, with the help of Wolfram Mathematica 9 software, the powerful sine-Gordon expansion method is used in constructing new hyperbolic function solutions to the two well known nonlinear differential equations that arise in the field of nonlinear sciences, namely; the modified Zakharov–Kuznetsov and the (2+1)-dimensional cubic Klein–Gordon equations. We also plot the two- and three-dimensional graphics of all the obtained solutions in this paper by utilizing the same program in the Wolfram Mathematica 9 software.

AtıfScopus17·WoS18·OpenAlex19

İncele

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan

In this paper, with the help of Wolfram Mathematica 9 we employ the powerful sine-Gordon expansion method in investigating the solution structures of the two well known nonlinear evolution equations, namely; Calogero–Bogoyavlenskii–Schiff and Kadomtsev–Petviashvili hierarchy equations. We obtain new solutions with complex, hyperbolic and trigonometric function structures. All the obtained solutions in this paper verified their corresponding equations. We also plot the three- and two-dimensional graphics of all the obtained solutions in this paper by using the same program in Wolfram Mathematica 9. We finally submit a comprehensive conclusion.

AtıfScopus42·WoS44·OpenAlex56

İncele

Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Erdogan, Fevzi; Mehmet Baskonus, Haci

With the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is used in constructing some new solutions to the two well-known nonlinear models, namely, the simplified modified Camassa-Holm and symmetric regularized long-wave equations. We obtain some novel complex, trigonometric and hyperbolic function solutions to these two equations. We also plot the three-dimensional and two-dimensional graphics for each solutions obtained using the same programming code in Wolfram Mathematica software. Finally, we submit a comprehensive conclusions.

AtıfScopus30·OpenAlex31

İncele

Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet

In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.

AtıfScopus54·WoS51·OpenAlex53

İncele

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan

In this paper, we seek for the new soliton solutions to the coupled nonlinear Maccari's system by using sine-Gordon expansion method. Sine-Gordon expansion method is based on sine-Gordon Eq. (2.1) and a travelling wave transformation. We obtain new complex hyperbolic functions solutions to this system with help of Wolfram Mathematica 9, we also plot 3-dimensional and 2-dimensional graphics to some obtained solution using the same program in Wolfram Mathematica 9. Finally, we submit a comprehensive conclusions.

AtıfScopus83·WoS85·OpenAlex90

İncele

Baskonus, Haci Mehmet; Bulut, Hasan; Sulaiman, Tukur Abdulkadir

In this paper, with the aid of the Wolfram Mathematica 9 program, we obtain some novel complex hyperbolic function solutions to the extended (2+1)-dimensional quantum Zakharov-Kuznetsov equation by using the sine-Gordon expansion method. We find some complex and hyperbolic function solutions. Subsequently, we plot 2D surfaces representing the obtained solutions by considering some suitable values of the parameters. At the end of this paper, we compare our results with the existing results in the literature by presenting comprehensive conclusions.

AtıfScopus38·WoS36·OpenAlex50

İncele

Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet

In this manuscript, we apply the powerful sine-Gordon expansion method to the Korteweg–de Vries (KdV) equation with dual-power law nonlinearity. The method is a combination of the travelling wave transformation and sine-Gordon equation. We find some new complex solitary and optical wave solution structures to the KdV equation with dual-power law nonlinearity. Wolfram Mathematica 9 is used in carrying out all the computations and the graphics plot in this paper. We have finally submit a comprehensive conclusion.

AtıfScopus63·WoS61·OpenAlex77

İncele