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- MakaleAçık Erişim2017Scopus SJRQ3New solitary wave solutions to the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff and the Kadomtsev–Petviashvili hierarchy equations
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.
AtıfScopus42WoS44OpenAlex56
İncele - 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