scholarly journals Improved hyperbolic function method and exact solutions for variable coefficient Benjamin-Bona-Mahony-Burgers equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1183-1187
Author(s):  
Hong-Cai Ma ◽  
Xiao-Fang Peng ◽  
Dan-Dan Yao
Keyword(s):  
Fluid Mechanics ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Function Method ◽  
Burgers Equation ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Hyperbolic Function Method

By using the improved hyperbolic function method, we investigate the variable coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.

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 The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Yong Huang ◽  
Yadong Shang
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Function Method ◽  
Hyperbolic Function ◽  
Nonlinear Heat Conduction ◽  
Hyperbolic Function Method

The extended hyperbolic function method is used to derive abundant exact solutions for generalized forms of nonlinear heat conduction and Huxley equations. The extended hyperbolic function method provides abundant solutions in addition to the existing ones. Some previous results are supplemented and extended greatly.

Regarding Rational Exponential and Hyperbolic Functions Solutions of Conformable Time-Fractional Phi-four Equation

2018 ◽  
Author(s):  
Asim Zafar ◽  
Alper Korkmaz ◽  
Bushra Khalid ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Function Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Hyperbolic Function Method ◽  
Projected Methods

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

VARIABLE-COEFFICIENT FORCED BURGERS SYSTEM IN NONLINEAR FLUID MECHANICS AND ITS POSSIBLY OBSERVABLE EFFECTS

2003 ◽  
Vol 14 (09) ◽  
pp. 1207-1222 ◽  
Author(s):  
YI-TIAN GAO ◽  
XIAO-GE XU ◽  
BO TIAN
Keyword(s):  
Variable Coefficient ◽  
Burgers Equation ◽  
Analytic Solutions ◽  
Charge Density Waves ◽  
Hyperbolic Function ◽  
Disordered Solids ◽  
Exact Analytic Solutions ◽  
Hyperbolic Function Method ◽  
Wu Method ◽  
Nonlinear Fluid

The forced Burgers equation works as a testing ground for a real turbulence, and as the qualitative model for a wide variety of problems including charge density waves, vortex lines in superconductors, disordered solids and epitaxial growth, etc. Its variable-coefficient generalizations call for better modeling of the physical situations. In this paper, we investigate a variable-coefficient generalization of the forced Burgers equation, and obtain several sets of exact soliton-like and other exact analytic solutions, via the extension of a generalized hyperbolic-function method with computerized symbolic computation. We also discuss the Wu method. We find some possibly observable effects, which might be discovered with the relevant experiments.

SPATIAL XPM-PAIRED SOLITONS IN NONLINEAR METAMATERIALS

2013 ◽  
Vol 22 (01) ◽  
pp. 1350009
Author(s):  
ANLE FANG ◽  
YUANJIANG XIANG ◽  
BINXIAN ZHUANG ◽  
LEYONG JIANG ◽  
XIAOYU DAI ◽  
...  
Keyword(s):  
Refractive Index ◽  
Optical Fibers ◽  
Function Method ◽  
Hyperbolic Function ◽  
Nonlinear Polarization ◽  
Dark Solitons ◽  
Nonlinear Metamaterials ◽  
Theoretical Predictions ◽  
Hyperbolic Function Method ◽  
Propagation Properties

We investigate spatial XPM-paired solitons in nonlinear metamaterials (MMs) based on the (1 + 1)-dimensional coupled nonlinear Schrodinger equation (NLSE) describing the co-propagation of two optical beams of different frequencies in the MM with a Kerr-type nonlinear polarization. Three types of XPM-paired solitons including bright-bright, bright-dark and dark-dark solitons for different combination of the signs of refractive index experienced by the two beams, respectively, are obtained by using a generalized hyperbolic function method, which makes the temporal XPM-paired solitons in optical fibers find their spatial counterparts in MMs. Numerical simulations are performed to confirm the theoretical predictions and further identify the propagation properties of the spatial XPM-paired solitons in MMs described by Drude model.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

A modified hyperbolic function method and its application to the Toda lattice

2006 ◽  
Vol 172 (2) ◽  
pp. 938-945 ◽  
Author(s):  
Hongyan Zhi ◽  
Xueqin Zhao ◽  
Zhongyuan Yang ◽  
Hongqing Zhang
Keyword(s):  
Function Method ◽  
Toda Lattice ◽  
Hyperbolic Function ◽  
Hyperbolic Function Method
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