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The basic principle of this study is to obtain various solutions to the (1+1) dimensional Mikhailov-Novikov-Wang integrable equation (MNWIE). For this purpose, the generalized exponential rational function method (GERFM) is applied to this equation. Thus, several trigonometric functions, hyperbolic functions, and dark soliton solutions to the studied equation are acquired. In this way, some new solutions to the equation that have not been presented before have been obtained. In addition, 2D and 3D graphics of the acquired solutions are drawn for specific values. The obtained results and the graphic drawings of the results have been provided by using Wolfram Mathematica 12. [ABSTRACT FROM AUTHOR]

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

In this paper, modified exp (-Ω(ξ))-expansion function method (MEFM) has been tackled for procuring exact solutions of (4+1) dimensional Fokas equation. Hyperbolic function solutions and dark soliton solutions of (4+1) dimensional Fokas equation have been found by means of this method. Moreover, by the help of Mathematica 9, some graphical simulations were given to clarify the behavior of these solutions.

Modified trial equation method (MTEM) was used for exact solutions of (2+1)-dimensional Zakharov-Kuznetsov (ZK) equation and Chafee-Infante equation. Three and two dimensional graphs were plotted to analyze the physical behaviors of the solutions by using Wolfram Mathematica 9.This method is an important method for finding travelling wave solutions of nonlinear partial differential equations (NLPDEs). [ABSTRACT FROM AUTHOR]

Studies in recent years have examined the analytical solutions of nonlinear evolution equations (NLEEs). These equations are handled by using a lot of methods. Especially, hyperbolic function solutions, soliton solutions and others have been revealed for these NLEEs. A powerful technique is used to attain some exact solutions of Nizhnik-Novikov-Veselov (NNV) system. Hyperbolic function solutions and dark soliton solutions of this system are constructed via modified exp(-Ω(ζ))-expansion function method (MEFM). Then, results that we obtained are submitted. Moreover, we draw 2D and 3D surfaces of some analytical solutions that we procured with the help of this method. [ABSTRACT FROM AUTHOR]

This study bases attention on new analytical solutions of Phi-four equation. The modified exp (-Ω(ξ)) -expansion function method (MEFM) has been used to obtain analytical solutions of the Phi-four equation. By using this method, dark soliton solutions and trigonometric function solution of the Phi-four equation have been found. [ABSTRACT FROM AUTHOR]

This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to highfrequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions. [ABSTRACT FROM AUTHOR]

In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods. [ABSTRACT FROM AUTHOR]

In this paper, we have obtained approximate solution of the nonlinear (3+1)-dimensional breaking soliton Equation (BSE) by using Homotopy Perturbation Method (HPM) and then formed a chart including numerical conclusion for this equation by drawing graphics of the the obtained solution by means of programming language Mathematica. [ABSTRACT FROM AUTHOR]

The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions. [ABSTRACT FROM AUTHOR]

In this paper, modified exp(-Ω(ξ))-expansion function method has been handled for finding exact solutions of positive Gardner-KP equation. Hyperbolic function solutions and dark soliton solution of positive Gardner-KP equation have been obtained by means of this method. Moreover, by the help of Mathematica 9, certain graphical notations were given to clarify the action of these solutions. [ABSTRACT FROM AUTHOR]