Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation

2021 ◽  
pp. 2150477
Author(s):  
Serbay Duran ◽  
Asif Yokuş ◽  
Hülya Durur
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Stationary Wave ◽  
Traveling Wave Solution ◽  
Incoming Wave ◽  
Topological Soliton ◽  
Advantages And Disadvantages ◽  
Wave Event ◽  
Ostrovsky Equation ◽  
General Graphs

In this study, we have taken into account the time-fractional Ostrovsky–Benjamin–Bona–Mahony equation, which is a synthesis of the time-fractional Ostrovsky equation and time-fractional Benjamin–Bona–Mahony equations and contains both mathematical and physical properties. Traveling wave solutions are produced by using the Ostrovsky–Benjamin–Bona–Mahony equation that physically sheds light on the incoming wave event on the ocean surface, using the sub-equation and Bernoulli sub-equation function methods. These solutions are presented in hyperbolic, trigonometric, singular and dark (topological) soliton types. With the help of special values given to the coefficients in the solitons obtained, it is associated with the solutions in the literature and it is observed that the solitons produced in this study are more general. Graphs representing the stationary wave at any given moment are presented. The advantages and disadvantages as well as the similarities and differences of the method are discussed in detail. Also, the behavior of the wave and its refraction according to the velocity variable, which is a physically important factor of the traveling wave solution, is analyzed and supported by simulation.

Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

2021 ◽  
pp. 2150213
Author(s):  
Hülya Durur
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Energy Transport ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Wave Solutions ◽  
Package Program

In this study, the Lonngren-wave equation, which is physically semiconductor, is taken into consideration. Traveling wave solutions of this equation are presented with generalized exponential rational function method, which is one of the mathematically powerful analytical methods. These solutions are produced in bright (non-topological) soliton and complex trigonometric-type traveling wave solutions. Three-dimensional (3D), 2D and contour graphics are presented with the help of a ready-made package program with special values given to constants in these solutions. The effect of the change in wave velocity on the traveling wave solution showing energy transport is presented with the help of simulation. It is argued that velocity is one of the important factors in wave diffraction. In the results and discussion section, the advantages and disadvantages of the method are discussed.

scholarly journals Simulation and refraction event of complex hyperbolic type solitary wave  in plasma and obtical fiber for the perturbed Chen-Lee-Liu equation

2021 ◽  
Author(s):  
Asıf Yokuş ◽  
Hülya Durur ◽  
Serbay Duran
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Hyperbolic Type ◽  
Traveling Wave Solution ◽  
Algebraic Equations ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Special Values ◽  
Analytic Methods

Abstract In this presented article, modified 1/G'-expansion and modified Kudryashov methods are applied to generate traveling wave solutions of perturbed Chen-Lee-Liu (CLL) equation. The similar and different aspects of the solutions produced by both analytic methods are discussed in the results and discussion section. By giving special values to the constants in the solutions obtained by analytical methods, 2D, 3D and contour graphics representing the shape of the standing wave at any time are presented. Additionally, the advantages and disadvantages of the two analytic methods are discussed and presented in the results and discussion section. Also, a solitary wave is produced by giving special values ​​to the parameters in the hyperbolic type complex traveling wave solution. Simulations are created for different values ​​of the frequency and velocity propagation parameters of the solitary wave. The values ​​of these parameters are calculated for the breakage event physically. A computer package program is used for operations such as solving complex operations, drawing graphics and systems of algebraic equations.

An investigation of the physical dynamics of a traveling wave solution called a bright soliton

2021 ◽  
Vol 96 (12) ◽  
pp. 125251
Author(s):  
Serbay Duran
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Applied Mathematics ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Kink Wave Solution ◽  
Advantages And Disadvantages ◽  
Kink Wave ◽  
Mathematics And Physics

Abstract This study examines the 1 + 2 -dimensional Zoomeron equation, which has recently become popular in applied mathematics and physics. Bright soliton (non-topological), kink wave solution and traveling wave solutions are generated with the advantages of the generalized exponential rational function method. With the help of this method, it is aimed to produce different types of solutions for the Zoomeron equation compared to other traditional exponential function methods. The effects of parameters on the amplitude of the wave function are discussed, along with physical explanations backed by simulations. In addition, the advantages and disadvantages of the method for the 1 + 2 -dimensional Zoomeron equation are discussed.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

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.

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050282
Author(s):  
Asıf Yokuş ◽  
Doğan Kaya
Keyword(s):  
Traveling Wave ◽  
Numerical Solutions ◽  
Traveling Wave Solutions ◽  
Transformation Method ◽  
Mkdv Equation ◽  
Traveling Wave Solution ◽  
Von Neumann ◽  
Wave Solutions ◽  
De Vries ◽  
The Stability

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

scholarly journals Approximate Damped Oscillatory Solutions for Generalized KdV-Burgers Equation and Their Error Estimates

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Weiguo Zhang ◽  
Xiang Li
Keyword(s):  
Dynamical Systems ◽  
Error Estimates ◽  
Traveling Wave ◽  
Wave Solution ◽  
Burgers Equation ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Traveling Wave Solution ◽  
Oscillatory Solutions ◽  
Wave Solutions

We focus on studying approximate solutions of damped oscillatory solutions of generalized KdV-Burgers equation and their error estimates. The theory of planar dynamical systems is employed to make qualitative analysis to the dynamical systems which traveling wave solutions of this equation correspond to. We investigate the relations between the behaviors of bounded traveling wave solutions and dissipation coefficient, and give two critical valuesλ1andλ2which can characterize the scale of dissipation effect, for right and left-traveling wave solution, respectively. We obtain that for the right-traveling wave solution if dissipation coefficientα≥λ1, it appears as a monotone kink profile solitary wave solution; that if0<α<λ1, it appears as a damped oscillatory solution. This is similar for the left-traveling wave solution. According to the evolution relations of orbits in the global phase portraits which the damped oscillatory solutions correspond to, we obtain their approximate damped oscillatory solutions by undetermined coefficients method. By the idea of homogenization principle, we give the error estimates for these approximate solutions by establishing the integral equations reflecting the relations between exact and approximate solutions. The errors are infinitesimal decreasing in the exponential form.

scholarly journals Existence of Traveling Wave Solutions for Cholera Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou ◽  
Xiaoli Wang
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Shooting Method ◽  
Reproduction Number ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion Model ◽  
Minimal Wave Speed ◽  
The Basic Reproduction Number

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.

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