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

In this paper, we study the generalized higher-order nonlinear Schrödinger equation analytically. We use two integral schemes for conducting this study. Dark, bright, combined dark–bright optical, singular soliton, soliton-like and trigonometric function solutions are successfully constructed. We give the constraint conditions for the existence of valid solutions. The 2D, 3D and the contour graphs for the dark and bright solitons are plotted.

AtıfScopus32·OpenAlex35

İncele

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

This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences.

AtıfScopus43·OpenAlex43

İncele

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

The dynamical systems of soliton propagation through optical fibers for trans-continental and trans-oceanic distances is one of the most interesting areas of study. Optical solitons are restrained electromagnetic waves that stretch in nonlinear dispersive media and allow the intensity to remain unchanged due to the balance between dispersion and nonlinearity effects. In this study, we successfully acquire dark, bright, combined dark–bright, singular and combined singular soliton solutions to the decoupled nonlinear Schrödinger equation arising in dual-core optical fibers by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid soliton solutions are given. We discuss how change in parameters affect the solitons transmission. We present the 2D, 3D and the contour graphs to some of the reported solutions.

AtıfScopus47·OpenAlex48

İncele

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

This study applies the powerful sine-Gordon expansion method in acquiring some new solutions to the strain wave equation in micro-structured solids arising in mathematical physics. The strain wave equation in micro-structured solids is used in modelling wave propagation in micro-structured materials. We successfully acquire some new solitary wave solutions with hyperbolic function structure. By taking some suitable values of parameters involved in the solutions, we plot the 2D, 3D and contour graphs of all the obtained solutions in this study.

AtıfScopus34·WoS34·OpenAlex36

İncele

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

This study investigates the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems by using the extended sinh-Gordon equation expansion method. The Nizhnik-Novikov-Veselov system is an isotropic Lax extension of the one-dimensional Korteweg-de Vries equation and the Drinfel’d-Sokolov system is a nonlinear model that possesses some special forms of Lax pairs. Topological kink-type, topological, non-topological, compound topological-non-topological bell-type and singular soliton solutions are successfully constructed. Under the choice of suitable values of parameters, the 2D, 3D and contour graphs to some of the obtained solutions are plotted.

AtıfScopus87·WoS94·OpenAlex101

İncele

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

This study constructs bright and singular optical solitons the (2 + 1)-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon expansion method. The parametric conditions for the existence of valid solitons are given. We give the variations of solitary and periodic wave solutions that depend on the parameters. We present the 2D, 3D and contour graphs to represent the kind of solutions secured in this study.

AtıfScopus40·OpenAlex41

İncele

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

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

Yel, Gülnur; Baskonus, Haci Mehmet; Bulut, Hasan

In this manuscript, we investigate the analytical solutions of the new coupled Konno–Oono equation by using the sine–Gordon expansion method. We successfully obtained some new soliton solutions to this model. We plot the 2D and 3D surfaces of all the found soliton solutions in this study. The Wolfram Mathematica 9 is used in performing all the computations in this study.

AtıfScopus99·WoS93

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