scholarly journals An Efficient Method for Analytically Solving (1+2)-dimensional Chiral Non-linear Schrödinger Equation

2022 ◽  
Author(s):  
Muslum Ozisik ◽  
Mustafa Bayram ◽  
Aydin Secer ◽  
Melih Cinar
Keyword(s):  
Algebraic Equation ◽  
Efficient Method ◽  
Traveling Wave ◽  
Expansion Method ◽  
Wave Theory ◽  
Equation System ◽  
Analytic Solutions ◽  
Wave Transformation ◽  
Nls Equation ◽  
Non Linear

Abstract In this paper, we have successfully extracted novel analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger (NLS) equation by modified extended tanh expansion method combined with new Riccati solutions (METEM-cNRCS) as far as we know. When a wave transformation is applied to the considered Chiral NLS equation, a nonlinear ODE is obtained. Assuming the solutions of ODE have a form as the method suggests, and substituting the trial solutions to the ODE, we get a polynomial. Gathering the coefficients with the same power in the polynomial, we acquire an algebraic equation system. So, we may obtain the abundant solutions of the (1+2)-dimensional Chiral NLS equation by solving the system via Maple. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper are a guide for future works in traveling wave theory.

scholarly journals An effective technique for the conformable space-time fractional EW and modified EW equations

2019 ◽  
Vol 8 (1) ◽  
pp. 157-163 ◽  
Author(s):  
K. Hosseini ◽  
A. Bekir ◽  
F. Rabiei
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Traveling Wave ◽  
Expansion Method ◽  
Space Time ◽  
Wave Transformation ◽  
Nonlinear Ordinary Differential Equations ◽  
Effective Technique ◽  
Fractional Models

AbstractThe current work deals with the fractional forms of EW and modified EW equations in the conformable sense and their exact solutions. In this respect, by utilizing a traveling wave transformation, the governing space-time fractional models are converted to the nonlinear ordinary differential equations (NLODEs); and then, the resulting NLODEs are solved through an effective method called the exp(−ϕ(ϵ))-expansion method. As a consequence, a number of exact solutions to the fractional forms of EW and modified EW equations are generated.

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. 

Dynamic interaction of behaviors of time-fractional shallow water wave equation system

2021 ◽  
pp. 2150353
Author(s):  
Serbay Duran
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Wave Transformation ◽  
Trigonometric Functions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by [Formula: see text]-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

scholarly journals Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 908 ◽  
Author(s):  
Asıf Yokus ◽  
Hülya Durur ◽  
Hijaz Ahmad ◽  
Shao-Wen Yao
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Solution Process ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Nonlinear Evolution Equations ◽  
Important Place ◽  
Advantages And Disadvantages ◽  
Wave Solutions

In this paper, a new solution process of ( 1 / G ′ ) -expansion and ( G ′ / G , 1 / G ) -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical ( G ′ / G , 1 / G ) -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave solutions, whereas traveling wave has an important place in applied sciences and illuminates many physical phenomena. 3D, 2D and contour graphs are displayed to show the stationary wave or the state of the wave at any moment with the values given to these constants. Conditions that guarantee the existence of traveling wave solutions are given. Comparison of ( G ′ / G , 1 / G ) -expansion method and ( 1 / G ′ ) -expansion method, which are important instruments in the analytical solution, has been made. In addition, the advantages and disadvantages of these two methods have been discussed. These methods are reliable and efficient methods to obtain analytic solutions of nonlinear evolution equations (NLEEs).

Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method

2019 ◽  
Vol 34 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Hülya Durur
Keyword(s):  
Applied Sciences ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Important Place ◽  
Wave Solutions ◽  
Different Types ◽  
Hyperbolic Complex ◽  
Rational Type

In this paper, an alternative method has been studied for traveling wave solutions of mathematical models which have an important place in applied sciences and balance term is not integer. With this method, the trigonometric, hyperbolic, complex and rational type traveling wave solutions of the (1[Formula: see text]+[Formula: see text]1)-dimensional resonant nonlinear Schrödinger’s (RNLS) equation with the parabolic law have constructed. This method can be applied reliably and effectively in many differential equations.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals Hydromechanical Structure of the Cochlea Supports the Backward Traveling Wave in the Cochlea In Vivo

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Fangyi Chen ◽  
Dingjun Zha ◽  
Xiaojie Yang ◽  
Allyn Hubbard ◽  
Alfred Nuttall
Keyword(s):  
Traveling Wave ◽  
Basilar Membrane ◽  
Wave Theory ◽  
Otoacoustic Emission ◽  
Traditional Theory ◽  
Vibration Source ◽  
Ear Canal ◽  
Local Vibration ◽  
Membrane Vibration

The discovery that an apparent forward-propagating otoacoustic emission (OAE) induced basilar membrane vibration has created a serious debate in the field of cochlear mechanics. The traditional theory predicts that OAE will propagate to the ear canal via a backward traveling wave on the basilar membrane, while the opponent theory proposed that the OAE will reach the ear canal via a compression wave. Although accepted by most people, the basic phenomenon of the backward traveling wave theory has not been experimentally demonstrated. In this study, for the first time, we showed the backward traveling wave by measuring the phase spectra of the basilar membrane vibration at multiple longitudinal locations of the basal turn of the cochlea. A local vibration source with a unique and precise location on the cochlear partition was created to avoid the ambiguity of the vibration source in most previous studies. We also measured the vibration pattern at different places of a mechanical cochlear model. A slow backward traveling wave pattern was demonstrated by the time-domain sequence of the measured data. In addition to the wave propagation study, a transmission line mathematical model was used to interpret why no tonotopicity was observed in the backward traveling wave.

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