scholarly journals Soliton solutions of cubic-quintic nonlinear Schrödinger and variant boussinesq equations by the first integral method

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4199-4208 ◽  
Author(s):  
Aly Seadawy ◽  
A. Sayed
Keyword(s):  
Integral Method ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
First Integral ◽  
First Integral Method ◽  
Nonlinear Schrödinger ◽  
Variant Boussinesq Equations

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 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 The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shoukry Ibrahim Atia El-Ganaini
Keyword(s):  
Optical Fibers ◽  
Integral Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Higher Dimensions ◽  
First Integrals ◽  
First Integral Method ◽  
Nonlinear Schrödinger ◽  
Planar Systems

The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.

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.  

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