Applications of the first integral method to nonlinear evolution equations

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).

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

Advances in Difference Equations ◽

10.1186/s13662-019-2377-9 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 4

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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Dark and singular soliton solutions of perturbed Gerdjikov-Ivanov equation via the first integral method

International Journal of Physical Research ◽

10.14419/ijpr.v6i2.13829 ◽

2018 ◽

Vol 6 (2) ◽

pp. 60

Author(s):

Salam Subhaschandra Singh

Keyword(s):

Exact Solutions ◽

Integral Method ◽

Social Dynamics ◽

Nonlinear Evolution ◽

Soliton Solutions ◽

First Integral ◽

Science And Engineering ◽

First Integral Method ◽

Nonlinear Science ◽

Singular Soliton

This paper employs the first integral method in obtaining dark and singular soliton solutions of perturbed Gerdjikov-Ivanov equation showing that the method is a powerful tool for finding exact solutions of many nonlinear evolution (NLE) equations which are found in the studies of social dynamics, nonlinear science and engineering.

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

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i3.470 ◽

2015 ◽

Vol 11 (3) ◽

pp. 3134-3138 ◽

Cited By ~ 3

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 andÂ reliability of the method are tested by its applications to the Couple Boiti-Leon-PempinelliÂ System which plays an important role in mathematical physics.

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