Application of the modified exponential function method to the Cahn-Allen equation

2017 ◽  
Author(s):  
Hasan Bulut
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Exponential Function Method

scholarly journals A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 309-316
Author(s):  
Gülnur Yel ◽  
Tolga Aktürk
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Periodic Functions ◽  
New Approach ◽  
Wave Solutions ◽  
Exponential Function Method

AbstractIn this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

scholarly journals New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science

2017 ◽  
Vol 7 (3) ◽  
pp. 240-247 ◽  
Author(s):  
Serbay Duran ◽  
Muzaffer Askin ◽  
Tukur Abdulkadir Sulaiman
Keyword(s):  
Exponential Function ◽  
Physical Science ◽  
Function Method ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Nonlinear Media ◽  
Wolfram Mathematica ◽  
Ill Posed ◽  
Exponential Function Method

In manuscript, with the help of the Wolfram Mathematica 9, we employ the modified exponential function method in obtaining some new soliton solutions to the ill-posed Boussinesq equation arising in nonlinear media. Results obtained with use of technique, and also, surfaces for soliton solutions are given. We also plot the 3D and 2D of each solution obtained in this study by using the same program in the Wolfram Mathematica 9.

scholarly journals Exact solutions of the 2+1-dimensional Camassa–Holm Kadomtsev–Petviashvili equation

2012 ◽  
Vol 17 (3) ◽  
pp. 280-296 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Nazila Yousefzadeh Fard ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Exponential Function ◽  
Soliton Solution ◽  
Function Method ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Petviashvili Equation ◽  
Exponential Function Method

This paper studies the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation. There are a few methods that will be utilized to carry out the integration of this equation. Those are the G'/G method as well as the exponential function method. Subsequently, the ansatz method will be applied to obtain the topological soliton solution of this equation. The constraint conditions, for the existence of solitons, will also fall out of these.

scholarly journals Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+1)-dimensional

2021 ◽  
Vol 11 (1) ◽  
pp. 92-99
Author(s):  
Haci Mehmet Baskonus
Keyword(s):  
Exponential Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Wolfram Mathematica ◽  
Waves Propagation ◽  
Exponential Function Method ◽  
2D And 3D

In this manuscript, new dark and trigonometric function traveling wave soliton solutions to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by using the modified exponential function method are successfully obtained. Along with novel dark structures, trigonometric solutions are also extracted. For deeper investigating of waves propagation on the surface, 2D and 3D graphs along with contour simulations via computational programs such as Wolfram Mathematica, Matlap softwares and so on are presented.

scholarly journals Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 176
Author(s):  
Shumaila Javeed ◽  
Khurram Saleem Alimgeer ◽  
Sidra Nawaz ◽  
Asif Waheed ◽  
Muhammad Suleman ◽  
...  
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Function Technique ◽  
Exponential Functions ◽  
Zk Equation ◽  
Exponential Function Method ◽  
Balancing Principle

This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.

scholarly journals Analytical method for nonlinear mathematical models with Atangana conformable derivative

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
pp. 040704
Author(s):  
T. Aktürk
Keyword(s):  
Exponential Function ◽  
Analytical Solutions ◽  
Function Method ◽  
Fractional Derivatives ◽  
Three Dimensional ◽  
Fractional Partial Differential Equations ◽  
Nonlinear Mathematical Models ◽  
Exponential Function Method ◽  
The Mathematical Model ◽  
Derivatives Of

In this study, we investigate the analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations, which are defined with Atangana conformable fractional derivative, using the modified exponential function method. Analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations were obtained by using the modified exponential function method. Two, three-dimensional and contour graphics are used to understand the physical interpretations of the resulting analytical solutions to the mathematical model. When all these results and graphs are analzyed, it has been shown that the modified exponential function method is an effective method for obtaining analytical solutions for all other nonlinear fractional partial differential equations containing conformable fractional derivatives of Atangana.

SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

2021 ◽  
Vol 10 (11) ◽  
pp. 3491-3504
Author(s):  
A. Darwish ◽  
H.M. Ahmed ◽  
M. Ammar ◽  
M.H. Ali ◽  
A.H. Arnous
Keyword(s):  
Periodic Solutions ◽  
Exponential Function ◽  
Spin Chain ◽  
Function Method ◽  
Chain Model ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Spin Chain Model ◽  
Chain Equation

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

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