scholarly journals Study on Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter to Find the Exact Dynamic Wave Solutions

2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Md Ashik Iqbal ◽  
Ye Wang ◽  
Md Mamun Miah ◽  
Mohamed S. Osman
Keyword(s):  
Expansion Method ◽  
Vital Role ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Conformable Derivative ◽  
Wave Solutions ◽  
Soliton Wave Solutions ◽  
Kink Soliton ◽  
Variable G ◽  
Dynamic Wave

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable G’/G,  1/G-expansion method. The solutions of the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative play a vital role in many scientific occurrences. The regular dynamical wave solutions of the abovementioned equation imply three different fundamental functions, which are the trigonometric function, the hyperbolic function, and the rational function. These solutions are classified graphically into three categories, such as singular periodic solitary, kink soliton, and anti-kink soliton wave solutions. Furthermore, the effect of the fractional parameter on these solutions is discussed through 2D plots.

scholarly journals ON THE COMPLEX MIXED DARK-BRIGHT WAVE DISTRIBUTIONS TO SOME CONFORMABLE NONLINEAR INTEGRABLE MODELS

Fractals ◽  
2021 ◽  
pp. 2240018
Author(s):  
ARMANDO CIANCIO ◽  
GULNUR YEL ◽  
AJAY KUMAR ◽  
HACI MEHMET BASKONUS ◽  
ESIN ILHAN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Expansion Method ◽  
Research Paper ◽  
Trigonometric Function ◽  
Integrable Models ◽  
Hyperbolic Function ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Wave Solutions

In this research paper, we implement the sine-Gordon expansion method to two governing models which are the (2+1)-dimensional Nizhnik–Novikov–Veselov equation and the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. We use conformable derivative to transform these nonlinear partial differential models to ordinary differential equations. We find some wave solutions having trigonometric function, hyperbolic function. Under the strain conditions of these solutions obtained in this paper, various simulations are plotted.

scholarly journals New Improvement of the Expansion Methods for Solving the Generalized Fitzhugh-Nagumo Equation with Time-Dependent Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-35 ◽  
Author(s):  
Jalil Manafian ◽  
Mehrdad Lakestani
Keyword(s):  
Expansion Method ◽  
Travelling Wave ◽  
Trigonometric Function ◽  
Time Dependent ◽  
Hyperbolic Function ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Function Solution ◽  
Wave Solutions ◽  
Nagumo Equation

An improvement of the expansion methods, namely, the improved tan⁡Φξ/2-expansion method, for solving nonlinear second-order partial differential equation, is proposed. The implementation of the new approach is demonstrated by solving the generalized Fitzhugh-Nagumo equation with time-dependent coefficients. As a result, many new and more general exact travelling wave solutions are obtained including periodic function solutions, soliton-like solutions, and trigonometric function solutions. The exact particular solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. We obtained further solutions comparing this method with other methods. The results demonstrate that the new tan⁡Φξ/2-expansion method is more efficient than the Ansatz method and Tanh method applied by Triki and Wazwaz (2013). Recently, this method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. Abundant exact travelling wave solutions including solitons, kink, and periodic and rational solutions have been found. These solutions might play an important role in engineering fields. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear physics.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

Solitary wave solutions of (2+1)-dimensional Maccari system

2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Nonlinear Optics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.

scholarly journals New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using Extended F-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yinghui He ◽  
Yun-Mei Zhao ◽  
Yao Long
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Wave Model ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions

The F-expansion method is used to find traveling wave solutions to various wave equations. By giving more solutions of the general subequation, an extended F-expansion method is introduced by Emmanuel. In our work, a generalized KdV type equation of neglecting the highest-order infinitesimal term, which is an important water wave model, is discussed by using the extended F-expansion method. And when the parameters satisfy certain relations, some new exact solutions expressed by Jacobi elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

scholarly journals Exploration on traveling wave solutions to the 3rd-order klein–fock-gordon equation (KFGE) in mathematical physics

2020 ◽  
Vol 8 (1) ◽  
pp. 14 ◽  
Author(s):  
Nur Hasan Mahmud Shahen ◽  
Foyjonnesa . ◽  
Md. Habibul Bashar
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Dynamic Models ◽  
Gordon Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Analytic Solutions ◽  
Hyperbolic Function ◽  
Wave Solutions

In this paper, the -expansion method has been applied to find the new exact traveling wave solutions of the nonlinear evaluation equations (NLEEs) by utilizing 3rd-order Klein–Gordon Equation (KFGE). With the collaboration of symbolic commercial software maple, the competence of this method for inventing these exact solutions has been more exhibited. As an upshot, some new exact solutions are obtained and signified by hyperbolic function solutions, different combinations of trigonometric function solutions, and exponential function solutions. Moreover, the -expansion method is a more efficient method for exploring essential nonlinear waves that enrich a variety of dynamic models that arises in nonlinear fields. All sketching is given out to show the properties of the innovative explicit analytic solutions. Our proposed method is directed, succinct, and reasonably good for the various nonlinear evaluation equations (NLEEs) related treatment and mathematical physics also. 

scholarly journals Complex Acoustic Gravity Wave Behaviors to a Mathematical Model Arising in Nonlinear Mathematical Physics

2018 ◽  
Vol 22 ◽  
pp. 01032
Author(s):  
Tolga Akturk ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Hasan Bulut
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Physical Interpretation ◽  
Physical Meaning ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Acoustic Gravity Wave ◽  
Mathematica Software

In this article, we utilize the powerful sine-Gordon expansion method (SGEM) in constructing some new solutions to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation by using the Mathematica software. We successfully obtain some new travelling solutions bearing some new structures such as trigonometric function, exponential function and hyperbolic function structures. We claim that some of our results are complex in structure. All the solutions obtained verified the the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. To illustrate our results, present the numerical simulation of all the obtained solutions in this study by selecting appropriate values of the parameters. Furthermore, we give the physical interpretation of all the graphics. We also give the physical meaning to some of the obtained results in this study.

scholarly journals Traveling Wave Solutions of Nonlinear Evolution Equation via Enhanced(G’/G)- Expansion Method

2014 ◽  
Vol 33 ◽  
pp. 83-92 ◽  
Author(s):  
Md. Ekramul Islam ◽  
Kamruzzaman Khan ◽  
M Ali Akbar ◽  
Rafiqul Islam
Keyword(s):  
Rational Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Wave Solutions

In this article, the Enhanced (G'/G)-expansion method has been projected to find the traveling wave solutions for nonlinear evolution equations(NLEEs) via the (2+1)-dimensional Burgers equation. The efficiency of this method for finding these exact solutions has been demonstrated with the help of symbolic computation software Maple. By this method we have obtained many new types of complexiton soliton solutions, such as, various combinations of trigonometric periodic function and rational function solutions, various combination of hyperbolic function and rational function solutions. The proposed method is direct, concise and effective, and can be used for many other nonlinear evolution equations. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 83-92 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17662

Sign in / Sign up

Export Citation Format

Share Document