scholarly journals Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Tianyong Han ◽  
Zhao Li
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Hyperbolic Function ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
System Method ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Complete Discrimination System

In this paper, the complete discrimination system method is used to construct the exact traveling wave solutions for fractional coupled Boussinesq equations in the sense of conformable fractional derivatives. As a result, we get the exact traveling wave solutions of fractional coupled Boussinesq equations, which include rational function solutions, Jacobian elliptic function solutions, implicit solutions, hyperbolic function solutions, and trigonometric function solutions. Finally, the obtained solution is compared with the existing literature.

Exact traveling wave solutions of partial differential equations with power law nonlinearity

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
H. Aminikhah ◽  
B. Pourreza Ziabary ◽  
H. Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Hyperbolic Function ◽  
Mathematical Tool ◽  
Partial Differential ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

AbstractIn this paper, we applied the functional variable method for four famous partial differential equations with power lawnonlinearity. These equations are included the Kadomtsev-Petviashvili, (3+1)-Zakharov-Kuznetsov, Benjamin-Bona-Mahony-Peregrine and Boussinesq equations. Various exact traveling wave solutions of these equations are obtained that include the hyperbolic function solutions and the trigonometric function solutions. The solutions shown that this method provides a very effective, simple and powerful mathematical tool for solving nonlinear equations in various fields of applied sciences.

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 On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

2017 ◽  
Vol 7 (3) ◽  
pp. 265-270
Author(s):  
Gülnur Yel ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Trigonometric Function ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this work, we construct the exact traveling wave solutions of the fractional (2+1)-dimensional Davey-Stewartson equation system (D-S) that is complex equation system using the Modified Trial Equation Method (MTEM). We obtained trigonometric function solutions by this method that are new in literature.

scholarly journals Applications of an Extended -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
E. M. E. Zayed ◽  
Shorog Al-Joudi
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Expansion Method ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Soliton Equation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Hyperbolic Function Solutions

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended -expansion method, whereGsatisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

scholarly journals Exact Single Traveling Wave Solutions for Generalized Fractional Gardner Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhao Li ◽  
Tianyong Han ◽  
Chun Huang
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Transformation ◽  
Wave Solutions ◽  
System Method ◽  
Order Polynomial ◽  
Complete Discrimination System ◽  
Fourth Order Polynomial

In this paper, the classification of all single traveling wave solutions to generalized fractional Gardner equations is presented by utilizing the complete discrimination system method. Under the fractional traveling wave transformation, generalized fractional Gardner equations can be reduced to an ordinary differential equations. All possible exact traveling wave solutions are given through the complete discrimination system of the fourth-order polynomial. Moreover, graphical representations of different kinds of the exact solutions reveal that the method is of significance for searching the exact solutions to generalized fractional Gardner equations.

scholarly journals Various Exact Solutions for the Conformable Time-Fractional Generalized Fitzhugh–Nagumo Equation with Time-Dependent Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sami Injrou ◽  
Ramez Karroum ◽  
Nadia Deeb
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Trigonometric Function ◽  
Time Dependent ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Rational Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Nagumo Equation

In this paper, the subequation method and the sine-cosine method are improved to give a set of traveling wave solutions for the time-fractional generalized Fitzhugh–Nagumo equation with time-dependent coefficients involving the conformable fractional derivative. Various structures of solutions such as the hyperbolic function solutions, the trigonometric function solutions, and the rational solutions are constructed. These solutions may be useful to describe several physical applications. The results show that these methods are shown to be affective and easy to apply for this type of nonlinear fractional partial differential equations (NFPDEs) with time-dependent coefficients.

scholarly journals Exact Solutions to the Sharma-Tasso-Olver Equation by Using ImprovedG′/G-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yinghui He ◽  
Shaolin Li ◽  
Yao Long
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Periodic Traveling Waves ◽  
Wave Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improvedG′/G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solutions are derived from the trigonometric function solutions. The improvedG′/G-expansion method is straightforward, concise and effective and can be applied to other nonlinear evolution equations in mathematical physics.

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