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 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.

Comparison Between Two Reliable Methods for Accurate Solution of Fractional Modified Fornberg–Whitham Equation Arising in Water Waves

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
A. K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Water Waves ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Accurate Solution ◽  
First Integral Method ◽  
Analytical Technique ◽  
Whitham Equation

In this paper, an analytical technique is proposed to determine the exact solution of fractional order modified Fornberg–Whitham equation. Since exact solution of fractional Fornberg–Whitham equation is unknown, first integral method has been applied to determine exact solutions. The solitary wave solution of fractional modified Fornberg–Whitham equation has been attained by using first integral method. The approximate solutions of fractional modified Fornberg–Whitham equation, obtained by optimal homotopy asymptotic method (OHAM), are compared with the exact solutions obtained by the first integral method. The obtained results are presented in tables to demonstrate the efficiency of these proposed methods. The proposed schemes are quite simple, effective, and expedient for obtaining solution of fractional modified Fornberg–Whitham equation.

scholarly journals Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

2012 ◽  
Vol 17 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Telegraph Equation ◽  
First Integral Method ◽  
Wave Solutions ◽  
Nonlinear Telegraph Equation

In this article we find the exact traveling wave solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation by using the first integral method. This method is based on the theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones.

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