Analytic treatment of nonlinear evolution equations using first integral method

Pramana ◽  
2012 ◽  
Vol 79 (1) ◽  
pp. 3-17 ◽  
Author(s):  
AHMET BEKIR ◽  
ÖMER ÜNSAL
Keyword(s):  
Integral Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
First Integral ◽  
Nonlinear Evolution Equations ◽  
First Integral Method ◽  
Analytic Treatment

scholarly journals Solutions of Kudryashov - Sinelshchikov equation and generalized Radhakrishnan-Kundu-Lakshmanan equation by the first integral method

2016 ◽  
Vol 4 (2) ◽  
pp. 37 ◽  
Author(s):  
Salam Subhaschandra Singh
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Integral Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Algebraic Method ◽  
First Integral ◽  
Nonlinear Evolution Equations ◽  
First Integral Method

This paper shows the applicability of the First Integral Method in obtaining solutions of Nonlinear Partial Differential Equations (NLPDEs). The method is applied in constructing solutions of Kudryashov-Sinelshchikov equation (KSE) and Generalized Radhakrishnan-Kundu-Lakshmanan Equation (GRKLE). The First Integral Method, which is based on the Ring Theory of Commutative Algebra, is a direct algebraic method for obtaining exact solutions of NLPDEs. This method is applicable to integrable as well as nonintegrable NLPDEs. The method is an efficient method for obtaining exact solutions of many Nonlinear Evolution Equations (NLEEs).

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 Optical soliton solutions to the $(2+1)$-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
M. Ali Akbar ◽  
Norhashidah Hj. Mohd. Ali ◽  
Jobayer Hussain
Keyword(s):  
Fiber Optics ◽  
Acoustic Waves ◽  
Integral Method ◽  
Soliton Solutions ◽  
First Integral ◽  
Nonlinear Evolution Equations ◽  
Dimensionless Form ◽  
Zakharov Equation ◽  
First Integral Method ◽  
Wave Solutions

Abstract The $(2+1)$ ( 2 + 1 ) -dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation have widespread scopes of function in science and engineering fields, such as in nonlinear fiber optics, the waves of electromagnetic field, plasma physics, the signal processing through optical fibers, fluid dynamics, coastal engineering and remarkable to model of the ion-acoustic waves in plasma, the sound waves. In this article, the first integral method has been assigned to search closed form solitary wave solutions to the previously proposed nonlinear evolution equations (NLEEs). We have constructed abundant soliton solutions and discussed the physical significance of the obtained solutions of its definite values of the included parameters through depicting figures and interpreted the physical phenomena. It has been shown that the first integral method is powerful, convenient, straightforward and provides further general wave solutions to diverse NLEEs in mathematical physics.

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