Generalized exponential rational function for distinct types solutions to the conformable resonant Schrödinger’s equation

2021 ◽  
Author(s):  
M. Eslami ◽  
A. Neirameh
Keyword(s):  
Rational Function ◽  
Fiber Optics ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Fiber Optics ◽  
Schrödinger’S Equation ◽  
Crystal Fibers ◽  
Mathematica Software ◽  
Schrödinger's Equation

The generalized exponential rational function method, which is one of the strong methods for solving nonlinear evolution equations, is applied to the conformable resonant nonlinear Schrödinger’s equation in this study. This equation plays a significant role in nonlinear fiber optics. It also has many important applications in photonic crystal fibers. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.

scholarly journals Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
First Time ◽  
Bbm Equation

Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.

scholarly journals The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yun-Mei Zhao ◽  
Ying-Hui He ◽  
Yao Long
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Simplest Equation Method ◽  
Klein Gordon ◽  
Schrödinger's Equation ◽  
Wave Reduction

A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.

Extended Transformed Rational Function Method to Nonlinear Evolution Equations

2019 ◽  
Vol 20 (6) ◽  
pp. 691-701 ◽  
Author(s):  
Emrullah Yaşar ◽  
Yakup Yıldırım ◽  
Abdullahi Rashid Adem
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Trigonometric Function ◽  
Nonlinear Evolution Equations ◽  
Bilinear Forms ◽  
Complexiton Solutions ◽  
Transformed Rational Function Method ◽  
Hirota Bilinear

AbstractIn this work, we study complexiton solutions to a (2+1)-dimensional (SK) equation and a (3+1)-dimensional nonlinear evolution equation. The complexiton solutions are combinations of trigonometric function waves and exponential function waves. For this goal, the extended transformed rational function method is carried out which is based on the Hirota bilinear forms of the considered equations and provides a systematical and convenient tool for constructing the exact solutions of nonlinear evolution equations.

scholarly journals Traveling Wave Solutions of Nonlinear Evolution Equation via Enhanced(G’/G)- Expansion Method

2014 ◽  
Vol 33 ◽  
pp. 83-92 ◽  
Author(s):  
Md. Ekramul Islam ◽  
Kamruzzaman Khan ◽  
M Ali Akbar ◽  
Rafiqul Islam
Keyword(s):  
Rational Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Wave Solutions

In this article, the Enhanced (G'/G)-expansion method has been projected to find the traveling wave solutions for nonlinear evolution equations(NLEEs) via the (2+1)-dimensional Burgers equation. The efficiency of this method for finding these exact solutions has been demonstrated with the help of symbolic computation software Maple. By this method we have obtained many new types of complexiton soliton solutions, such as, various combinations of trigonometric periodic function and rational function solutions, various combination of hyperbolic function and rational function solutions. The proposed method is direct, concise and effective, and can be used for many other nonlinear evolution equations. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 83-92 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17662

Application of Extended Transformed Rational Function Method to Some (3+1) Dimensional Nonlinear Evolution Equations

2018 ◽  
pp. 433-437
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Petviashvili Equation ◽  
Complexiton Solutions ◽  
Transformed Rational Function Method

The transformed rational function method can be considered as unification of the tanh type methods, the homogeneous balance method, the mapping method, the exp-function method and the F-expansion type methods. In this paper, we present complexiton solutions of (3+1) dimensional Korteweg-de Vries (KdV) equation and a new (3+1) dimensional generalized Kadomtsev-Petviashvili equation by using extended transformed rational function method which provides very useful and effective way to obtain complexiton solutions of nonlinear evolution equations.

scholarly journals The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 24-32 ◽  
Author(s):  
Aly Seadawy ◽  
Asghar Ali ◽  
Noufe Aljahdaly
Keyword(s):  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Wave Model ◽  
Nonlinear Evolution Equations ◽  
Mathematical Methods ◽  
Mathematica Software ◽  
Physical Phenomena ◽  
2D And 3D

AbstractIn this work, we construct traveling wave solutions of (1+1) - dimensional Ito integro-differential equation via three analytical modified mathematical methods. We have also compared our achieved results with other different articles. Portrayed of some 2D and 3D figures via Mathematica software demonstrates to understand the physical phenomena of the nonlinear wave model. These methods are powerful mathematical tools for obtaining exact solutions of nonlinear evolution equations and can be also applied to non-integrable equations as well as integrable ones. Hence worked-out results ascertained suggested that employed techniques best to deal NLEEs.

scholarly journals New optical solitons of conformable resonant nonlinear Schrödinger’s equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 761-769
Author(s):  
Hadi Rezazadeh ◽  
Reza Abazari ◽  
Mostafa M. A. Khater ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Schrödinger’S Equation ◽  
Wave Solutions ◽  
Functional Variable ◽  
Functional Variable Method ◽  
Schrödinger's Equation

AbstractSardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrödinger’s equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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