scholarly journals New soliton solutions of nonlinear Kudryashov's equation via Improved tan 􀀀 ( ) 2   -expansion approach in optical  ber

2021 ◽  
Author(s):  
Saima Arshed ◽  
◽  
Nauman Raza ◽  
Asma Rashid Butt ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Group Velocity ◽  
Traveling Wave ◽  
Graphical Representation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Erential Equation ◽  
Analytical Technique ◽  
The Given ◽  
Singular Soliton

In this article, a newly introduced model nonlinear Kudryashov's equation with anti-cubic non- linearity is considered for extraction of soliton solutions. This model is utilized to depict the propagation of modulated envelope signals which disseminate with some group velocity. To  nd a solution, an appropriate traveling wave hypothesis is used to covert the given model into a nonlinear ordinary di erential equation. An analytical technique, the Improved tan    ( ) 2   - expansion approach has been employed on the governing model to construct many new forms of dark soliton, singular soliton, periodic soliton, dark-singular combo soliton and rational solu- tion. The constraint conditions for the existence of these solitons have also been provided. The physical signi cance of the proposed equation has been provided with a graphical representation of the constructed solutions.

New soliton solutions of the CH–DP equation using Lie symmetry method

2018 ◽  
Vol 32 (20) ◽  
pp. 1850234 ◽  
Author(s):  
A. H. Abdel Kader ◽  
M. S. Abdel Latif
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Lie Symmetry ◽  
Jacobi Elliptic Functions ◽  
Lie Symmetry Method ◽  
Wave Solutions ◽  
Symmetry Method

In this paper, using Lie symmetry method, we obtain some new exact traveling wave solutions of the Camassa–Holm–Degasperis–Procesi (CH–DP) equation. Some new bright and dark soliton solutions are obtained. Also, some new doubly periodic solutions in the form of Jacobi elliptic functions and Weierstrass elliptic functions are obtained.

scholarly journals New and More Solitary Wave Solutions for the Klein-Gordon-Schrödinger Model Arising in Nucleon-Meson Interaction

2021 ◽  
Vol 9 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Asma Rashid Butt ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Art Integration ◽  
Scalar Mesons ◽  
Integration Schemes ◽  
Klein Gordon ◽  
Physical Features ◽  
Existence Criteria ◽  
Singular Soliton

This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.

scholarly journals Some analytical solutions by mapping methods for non-linear conformable time-fractional PHI-4 equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1815-1822 ◽  
Author(s):  
Zeliha Korpinar
Keyword(s):  
Fractional Derivative ◽  
Periodic Solutions ◽  
Soliton Solution ◽  
Analytical Solutions ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Conformable Fractional Derivative ◽  
Singular Soliton

In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-4 equation by means of conformable fractional derivative. The solutions are derived using Jacobi?s elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are iden?tified bright optical soliton, dark soliton, singular soliton, combo soliton solution, and periodic solutions.

Analytical soliton solutions and modulation instability for a generalized (3 + 1)-dimensional coupled variable-coefficient nonlinear Schrödinger equations in nonlinear optics

2021 ◽  
pp. 2050407
Author(s):  
A. A. Hamed ◽  
S. Shamseldeen ◽  
M. S. Abdel Latif ◽  
H. M. Nour
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Wave Parameter ◽  
Nonlinear Odes ◽  
Coupled Partial Differential Equations ◽  
Nonlinear Schrödinger ◽  
Schrödinger System

In this work, the soliton solutions of a (3 + 1)-dimensional coupled nonlinear Schrödinger system with time-dependent coefficients arising in optical fiber has been studied analytically. A complex traveling wave ansatz is used to transform the proposed coupled partial differential equations into ordinary differential equations (ODEs). Then, we solved the obtained nonlinear ODEs for the envelope function in the traveling wave parameter. The obtained waves envelope have the forms of bright and dark soliton-like solutions which are considered as new solutions of the studied system. As a kind of completing the analysis, the modulation instability is discussed based on the linear stability analysis.

scholarly journals A Generalized KdV Equation of Neglecting the Highest-Order Infinitesimal Term and Its Exact Traveling Wave Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xianbin Wu ◽  
Weiguo Rui ◽  
Xiaochun Hong
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Dynamic Properties ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Wave Model ◽  
Dark Soliton ◽  
Exact Traveling Wave Solutions ◽  
Generalized Kdv Equation ◽  
Wave Solutions

We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop-soliton solutions, broken loop-soliton solutions, broken wave solutions of U-form and C-form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical softwareMaple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.

scholarly journals Optical solitons to the fractional Schrödinger-Hirota equation

2019 ◽  
Vol 4 (2) ◽  
pp. 535-542 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Sibel Sehriban Atas
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Solitons ◽  
Hirota Equation ◽  
3 Dimensional ◽  
Peak Intensity ◽  
Singular Soliton

AbstractThis study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

scholarly journals Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1003-1010
Author(s):  
Asıf Yokuş ◽  
Hülya Durur ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah ◽  
Münevver Tuz ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Analytical Methods ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Mathematical Tool ◽  
Symbolic Calculation ◽  
Advantages And Disadvantages ◽  
Wave Solutions

Abstract In this article, the Sinh–Gordon function method and sub-equation method are used to construct traveling wave solutions of modified equal width equation. Thanks to the proposed methods, trigonometric soliton, dark soliton, and complex hyperbolic solutions of the considered equation are obtained. Common aspects, differences, advantages, and disadvantages of both analytical methods are discussed. It has been shown that the traveling wave solutions produced by both analytical methods with different base equations have different properties. 2D, 3D, and contour graphics are offered for solutions obtained by choosing appropriate values of the parameters. To evaluate the feasibility and efficacy of these techniques, a nonlinear evolution equation was investigated, and with the help of symbolic calculation, these methods have been shown to be a powerful, reliable, and effective mathematical tool for the solution of nonlinear partial differential equations.

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

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