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- MakaleAçık Erişim2018Scopus SJRQ2Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation
Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet
In this study, the applications of the extended sinh-Gordon equation expansion method to a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2 + 1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit is presented. We successfully construct dark, bright, combined dark-bright, singular and combined singular soliton solutions to this equation. We give the parametric conditions for the existence of valid soliton to each of the obtained solutions. We plot the 2D and 3D graphics to some of the obtained solutions. The reported results of this study may be helpful in explaining the physical meaning of the studied model.
AtıfScopus40WoS59OpenAlex73
İncele - MakaleAçık Erişim2018Scopus SJRQ2On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems
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.
AtıfScopus87WoS94OpenAlex101İncele - MakaleYayıncıda açık erişim2015ON SOME NEW ANALYTICAL SOLUTIONS FOR THE (2+1)-DIMENSIONAL BURGERS EQUATION AND THE SPECIAL TYPE OF DODD-BULLOUGH-MIKHAILOV EQUATION
Baskonus, Haci Mehmet; Bulut, Hasan
Some new travelling wave transform methods are very important for obtaining analytical solutions of special type of nonlinear partial differential equations (NLPDEs). Some of these solutions of NLPDEs may be in the different forms such as rational function solutions, trigonometric function solutions, hyperbolic function solutions, exponential function solutions and Jacobi elliptic function solutions. These forms tell us the various properties of the NLPDEs from scientifical applications to engineering. In this research, we have studied to obtain the analytical solution of the nonlinear (2+1)-dimensional Burgers equation which is named from Johannes Martinus Burgers and the nonlinear special type of the Dodd-Bullough-Mikhailov equation introduced to the literature by Roger Dodd, Robin Bullough, and Alexander Mikhailov.
AtıfWoS20İncele - MakaleAçık Erişim2015Scopus SJRQ2New Hyperbolic Function Solutions for Some Nonlinear Partial Differential Equation Arising in Mathematical Physics
Baskonus, Haci Mehmet; Bulut, Hasan
In this study, we investigate some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin-Bona-Mahony equation and the (2 + 1)-dimensional cubic Klein-Gordon equation by using the generalized Kudryashov method. After we submitted the general properties of the generalized Kudryashov method in Section 2, we applied this method to these problems to obtain some new analytical solutions, such as rational function solutions, exponential function solutions and hyperbolic function solutions in Section 3. Afterwards, we draw two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9.
AtıfWoS23OpenAlex33İncele