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.

OPTICAL SOLITON SOLUTIONS OF THE LONG-SHORT-WAVE INTERACTION SYSTEM

2013 ◽  
Vol 22 (02) ◽  
pp. 1350015 ◽  
Author(s):  
AHMET BEKIR ◽  
ESIN AKSOY ◽  
ÖZKAN GÜNER
Keyword(s):  
Soliton Solution ◽  
Function Method ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Short Wave ◽  
Optical Soliton ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Dependent Model

This paper, studies the long-short-wave interaction (LS) equation. An optical soliton solution is obtained by the exp-function method and the ansatz method. Subsequently, we formally derive the dark (topological) soliton solutions for this equation. By using the exp-function method, some additional solutions will be derived. The physical parameters in the soliton solutions of ansatz method: amplitude, inverse width, and velocity are obtained as functions of the dependent model coefficients.

scholarly journals Compactons and topological solitons of the Drinfel'd–Sokolov system

2014 ◽  
Vol 19 (2) ◽  
pp. 209-224
Author(s):  
Mustafa Inc ◽  
Eda Fendoglu ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Elliptic Function ◽  
Function Method ◽  
Soliton Solutions ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Topological Solitons ◽  
Wave Solutions

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions.

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 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.

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