scholarly journals Exact solutions with arbitrary functions of the (4+1)-dimensional fokas equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2403-2411 ◽  
Author(s):  
Bo Xu ◽  
Sheng Zhang
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Trigonometric Function ◽  
High Dimensional ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

In this paper, the (4+1)-dimensional Fokas equation is solved by the generalized F-expansion method, and new exact solutions with arbitrary functions are obtained. The obtained solutions include Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the generalized F-expansion method can be used for constructing exact solutions with arbitrary functions of some other high dimensional partial differential equations in fluids.

scholarly journals Exact Solutions for(4+1)-Dimensional Nonlinear Fokas Equation Using ExtendedF-Expansion Method and Its Variant

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yinghui He
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
New Exact Solutions ◽  
Higher Dimensional

The construction of exact solution for higher-dimensional nonlinear equation plays an important role in knowing some facts that are not simply understood through common observations. In our work,(4+1)-dimensional nonlinear Fokas equation, which is an important physical model, is discussed by using the extendedF-expansion method and its variant. And some new exact solutions expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

scholarly journals F-Expansion Method and Its Application for Finding New Exact Solutions to the Kudryashov-Sinelshchikov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
Trigonometric Functions ◽  
Extended Version ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions

Based on theF-expansion method, and the extended version ofF-expansion method, we investigate the exact solutions of the Kudryashov-Sinelshchikov equation. With the aid of Maple, more exact solutions expressed by Jacobi elliptic function are obtained. When the modulus m of Jacobi elliptic function is driven to the limits 1 and 0, some exact solutions expressed by hyperbolic function solutions and trigonometric functions can also be obtained.

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 The Improvedexp⁡-Φξ-Expansion Method and New Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Guiying Chen ◽  
Xiangpeng Xin ◽  
Hanze Liu
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

Theexp(-Φ(ξ))-expansion method is improved by presenting a new auxiliary ordinary differential equation forΦ(ξ). By using this method, new exact traveling wave solutions of two important nonlinear evolution equations, i.e., the ill-posed Boussinesq equation and the unstable nonlinear Schrödinger equation, are constructed. The obtained solutions contain Jacobi elliptic function solutions which can be degenerated to the hyperbolic function solutions and the trigonometric function solutions. The present method is very concise and effective and can be applied to other types of nonlinear evolution equations.

Exact Solutions for Coupled mKdV Equations by a New Symbolic Computation Method

2010 ◽  
Vol 20-23 ◽  
pp. 184-189 ◽  
Author(s):  
Bang Qing Li ◽  
Yu Lan Ma
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Evolution Equations ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Computation Method ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

By introducing (G′/G)-expansion method and symbolic computation software MAPLE, two types of new exact solutions are constructed for coupled mKdV equations. The solutions included trigonometric function solutions and hyperbolic function solutions. The procedure is concise and straightforward, and the method is also helpful to find exact solutions for other nonlinear evolution equations.

scholarly journals Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 871-880
Author(s):  
Bo Tang ◽  
Jiajia Tao ◽  
Shijun Chen ◽  
Junfeng Qu ◽  
Qian Wang ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Space Time ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Rational Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Physical Features

Abstract In the present study, we deal with the space–time fractional KdV–MKdV equation and the space–time fractional Konopelchenko–Dubrovsky equation in the sense of the conformable fractional derivative. By means of the extend \left(\tfrac{G^{\prime} }{G}\right) -expansion method, many exact solutions are obtained, which include hyperbolic function solutions, trigonometric function solutions and rational solutions. The results show that the extend \left(\tfrac{G^{\prime} }{G}\right) -expansion method is an efficient technique for solving nonlinear fractional partial equations. We also provide some graphical representations to demonstrate the physical features of the obtained solutions.

scholarly journals Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Phase Portraits ◽  
Hyperbolic Function ◽  
Bifurcation Method ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Reliable Methods

AbstractIn this paper, the bifurcation and new exact solutions for the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are investigated by utilizing two reliable methods, which are generalized $(G'/G)$ ( G ′ / G ) -expansion method and the integral bifurcation method. The exact solutions of the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are obtained by utilizing the generalized $(G'/G)$ ( G ′ / G ) -expansion method, these solutions are classified as hyperbolic function solutions, trigonometric function solutions, and rational function solutions. Giving different parameter conditions, many integral bifurcations, phase portraits, and traveling wave solutions for the equation are obtained via the integral bifurcation method. Graphical representations of different kinds of the exact solutions reveal that the two methods are of significance for constructing the exact solutions of fractional partial differential equation.

scholarly journals New Jacobi Elliptic Function Solutions for the Kudryashov-Sinelshchikov Equation Using Improved F-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yinghui He
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions

Based on the F-expansion method with a new subequation, an improved F-expansion method is introduced. As illustrative examples, some new exact solutions expressed by the Jacobi elliptic function of the Kudryashov-Sinelshchikov equation are obtained. When the modulusmof the Jacobi elliptic function is driven to the limits 1 and 0, some exact solutions expressed by hyperbolic function and trigonometric function can also be obtained. The method is straightforward and concise and is promising and powerful for other nonlinear evolution equations in mathematical 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.

Non-TravellingWave Solutions of the (2+1)-Dimensional Dispersive Long Wave System

2009 ◽  
Vol 64 (9-10) ◽  
pp. 540-552
Author(s):  
Mamdouh M. Hassan
Keyword(s):  
Expansion Method ◽  
Travelling Wave ◽  
Hyperbolic Function ◽  
Wave System ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Long Wave ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

With the aid of symbolic computation and the extended F-expansion method, we construct more general types of exact non-travelling wave solutions of the (2+1)-dimensional dispersive long wave system. These solutions include single and combined Jacobi elliptic function solutions, rational solutions, hyperbolic function solutions, and trigonometric function solutions.

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