scholarly journals The Investigation of Exact Solutions for the Appropriate Type of the Dispersive Long Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
J. Biazar ◽  
M. B. Mehrlatifan ◽  
Z. Salehdirin
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Expansion Method ◽  
First Integral ◽  
Travelling Wave ◽  
First Integral Method ◽  
Integral Methods ◽  
Division Theorem ◽  
Long Wave ◽  
The Given

Improved (G'/G)-expansion and first integral methods are used to construct exact solutions of the 2+1-dimensional Eckhaus-type extension of the dispersive long wave equation. The (G'/G)-expansion method is based on the assumptions that the travelling wave solutions can be expressed by a polynomial in (G'/G) and the first integral method is based on the theory of commutative algebra in which Division Theorem is of concern. It is worth mentioning that these methods are used for different systems and those two different systems can both be reduced to a system that will be mentioned in this paper. To recapitulate, this investigation has resulted in the exact solutions of the given systems.

scholarly journals Exact solutions of a class of nonlinear dispersive long wave systems via Feng's first integral method

2021 ◽  
Vol 6 (8) ◽  
pp. 7984-8000
Author(s):  
Qiuci Lu ◽  
◽  
Songchuan Zhang ◽  
Hang Zheng ◽  
Keyword(s):  
Exact Solutions ◽  
Integral Method ◽  
First Integral ◽  
First Integral Method ◽  
Long Wave

scholarly journals Exact Solutions of the Generalized KP-BBM Equation by the G′ / G-expansion Method and the First Integral Method

2018 ◽  
pp. 1-16
Author(s):  
Huaji Cheng ◽  
Yanxia Hu
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Integral Method ◽  
Expansion Method ◽  
First Integral ◽  
Hyperbolic Function ◽  
Rational Solutions ◽  
First Integral Method ◽  
Hyperbolic Function Solutions ◽  
Bbm Equation

In this paper, the generalized KP-BBM equation is considered. The G′ / G-expansion method and the first integral method are applied to integrate the equation. By means of the two methods, the rational solutions, the periodic solutions and the hyperbolic function solutions are thus obtained under some parametric conditions.

scholarly journals Exact Solutions of the Symmetric Regularized Long Wave Equation and the Klein-Gordon-Zakharov Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Isaiah Elvis Mhlanga ◽  
Chaudry Masood Khalique
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Symmetry Approach ◽  
New Exact Solutions ◽  
Long Wave ◽  
Simplest Equation Method ◽  
Regularized Long Wave Equation ◽  
Klein Gordon

We study two nonlinear partial differential equations, namely, the symmetric regularized long wave equation and the Klein-Gordon-Zakharov equations. The Lie symmetry approach along with the simplest equation and exp-function methods are used to obtain solutions of the symmetric regularized long wave equation, while the travelling wave hypothesis approach along with the simplest equation method is utilized to obtain new exact solutions of the Klein-Gordon-Zakharov equations.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

scholarly journals The first integral method and traveling wave solutions to Davey–Stewartson equation

2012 ◽  
Vol 17 (2) ◽  
pp. 182-193 ◽  
Author(s):  
Hossein Jafari ◽  
Atefe Sooraki ◽  
Yahya Talebi ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integral Method ◽  
Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

First integral method for non-linear differential equations with conformable derivative

2018 ◽  
Vol 13 (1) ◽  
pp. 14 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar ◽  
Abdon Atangana
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
General Scheme ◽  
First Integral ◽  
Fractional Partial Differential Equations ◽  
Conformable Derivative ◽  
First Integral Method ◽  
Analytic Treatment ◽  
Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

scholarly journals First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 783 ◽  
Author(s):  
Shumaila Javeed ◽  
Sidra Riaz ◽  
Khurram Saleem Alimgeer ◽  
M. Atif ◽  
Atif Hanif ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Dimensional Space ◽  
Nonlinear Partial Differential Equations ◽  
First Integral ◽  
Mathematical Physics ◽  
Space Time ◽  
Mathematical Tool ◽  
Long Wave ◽  
Higher Dimensional ◽  
Dimensional Space Time

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.

Optical solitons for coupled Fokas–Lenells equation in birefringence fibers

2019 ◽  
Vol 33 (26) ◽  
pp. 1950317 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Sultan Sial
Keyword(s):  
Integral Method ◽  
Expansion Method ◽  
First Integral ◽  
Optical Solitons ◽  
Optical Soliton ◽  
First Integral Method ◽  
Complexiton Solutions ◽  
Existence Criterion

This paper discusses bright, dark and singular optical soliton as well as complexiton solutions to the coupled Fokas–Lenells equation (FLE) for birefringent fibers by three integration tools such as [Formula: see text]-expansion method, the first integral method and the sine-Gordon expansion method. The existence criterion of these solutions is also given.

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