scholarly journals Exact soliton solutions of the modified KdV–KP equation and the Burgers–KP equation by using the first integral method

2011 ◽  
Vol 35 (8) ◽  
pp. 3991-3997 ◽  
Author(s):  
N. Taghizadeh ◽  
M. Mirzazadeh ◽  
F. Farahrooz
Keyword(s):  
Integral Method ◽  
Soliton Solutions ◽  
First Integral ◽  
Kp Equation ◽  
First Integral Method ◽  
Exact Soliton Solutions

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.

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

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.  

scholarly journals Dark soliton solutions to (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation via the first integral method

2020 ◽  
Vol 8 (2) ◽  
pp. 40
Author(s):  
Salam Subhaschandra Singh
Keyword(s):  
Soliton Solution ◽  
Integral Method ◽  
Soliton Solutions ◽  
First Integral ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Nls Equation ◽  
First Integral Method ◽  
Nonlinear Schrödinger ◽  
Trigonometric Solution

 In the present work, the First Integral Method is being applied in finding a non-soliton as well as a soliton solution of the ( 2 + 1 ) dimensional Kundu-Mukherjee-Naskar (KMN) equation which is a variant of the well-known Nonlinear Schrodinger ( NLS ) equation. Using the method, a dark optical soliton solution and a periodic trigonometric solution to the KMN equation have been suggested and the relevant conditions which guarantee the existence of such solutions are also indicated therein.  

scholarly journals The First Integral Method for Solving Maccari’s System

2011 ◽  
Vol 02 (02) ◽  
pp. 258-263 ◽  
Author(s):  
Davood Rostamy ◽  
Fatemeh Zabihi ◽  
Kobra Karimi ◽  
Siamak Khalehoghli
Keyword(s):  
Integral Method ◽  
First Integral ◽  
First Integral Method

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

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.

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