scholarly journals Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Nur Hasan Mahmud Shahen ◽  
Foyjonnesa ◽  
Md Habibul Bashar ◽  
Tasnim Tahseen ◽  
Sakhawat Hossain
Keyword(s):  
Rational Function ◽  
Fractional Order ◽  
Nonlinear Waves ◽  
Rogue Wave ◽  
Mathematical Physics ◽  
Kawahara Equation ◽  
Density Plot ◽  
Wave Solutions ◽  
Expansion Technique ◽  
Free Parameters

Utilizing of illustrative scheming programming, the study inspects the careful voyaging wave engagements from the nonlinear time fractional modified Kawahara equation (mKE) by employing the advanced exp − φ ξ -expansion policy in terms of trigonometric, hyperbolic, and rational function through some treasured fractional order derivative and free parameters. The undercurrents of nonlinear wave answer are scrutinized and confirmed by MATLAB in 3D and 2D plots, and density plot by specific values of the convoluted parameters is designed. Our preferred advanced exp − φ ξ -expansion technique which is parallel to ( G ′ / G ) expansion technique is trustworthy dealing for searching significant nonlinear waves that progress a modification of dynamic depictions that ascend in mathematical physics and engineering grounds.

Generalized exponential rational function method for extended Zakharov–Kuzetsov equation with conformable derivative

2019 ◽  
Vol 34 (20) ◽  
pp. 1950155 ◽  
Author(s):  
Behzad Ghanbari ◽  
M. S. Osman ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Function Method ◽  
Three Dimensional ◽  
Conformable Derivative ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Contour Plots ◽  
Free Parameters ◽  
Exponential Rational Function Method

In this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov–Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters.

Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system

2021 ◽  
Author(s):  
Serge P. Mukam ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
Victor K. Kuetche ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Higher Order ◽  
Lax Pairs ◽  
Wave Solutions ◽  
Free Parameters ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Physical Phenomena

In this paper, we propose a recursive Darboux transformation in a generalized form of a focusing vector Nonlinear Schrödinger Equation (NLSE) known as the Manakov System. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with a rule of iteration. We discuss from first- to three-order vector generalizations of rogue wave solutions while illustrating these features with some 3D, 2D graphical depictions. We illustrate a clear connection between higher-order rogue wave solutions and their free parameters for better understanding the physical phenomena described by the Manakov system

Kink Type Traveling Wave Solutions of Right-handed Non-commutative Burgers Equations via Extended (G0/G)-Expansion Method

2019 ◽  
pp. 1-6
Author(s):  
Harun-Or-Roshid .
Keyword(s):  
Traveling Wave ◽  
Gas Dynamics ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Free Parameters

The extended (G0 /G)-expansion method is significant for finding the exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we inhanced new traveling wave solutions of right-handed non-commutative burg- ers equations via extended (G0 /G)-expansion. Implementation of the method for searching exact solutions of the equation provided many new solutions which can be used to exploy some practically physical and machanical phenomena. Moreover, when the parameters are re- placed by special values, the well-known solitary wave solutions of the equation rediscovered from the traveling wave solutions and included free parameters may imply some physical meaningful results in fluid mechanics, gas dynamics, and traffic flow.

scholarly journals Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences

2021 ◽  
Vol 60 (2) ◽  
pp. 2687-2696
Author(s):  
Shahzad Sarwar ◽  
Khaled M. Furati ◽  
Muhammad Arshad
Keyword(s):  
Fractional Order ◽  
Wave Model ◽  
Space Time ◽  
Physical Sciences ◽  
Wave Solutions

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

A second-order three-wave interaction system and its rogue wave solutions

2021 ◽  
Author(s):  
Xianguo Geng ◽  
Yihao Li ◽  
Bo Xue
Keyword(s):  
Rogue Wave ◽  
Wave Interaction ◽  
Second Order ◽  
Wave Solutions ◽  
Interaction System ◽  
Rogue Wave Solutions
Sign in / Sign up

Export Citation Format

Share Document