scholarly journals Exact traveling wave solutions for a new nonlinear heat transfer equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1833-1838 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang ◽  
Yu-Feng Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Partial Differential Equation ◽  
Heat Transfer Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Transfer Problems

In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

scholarly journals New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Higher Dimensional

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

scholarly journals Exact traveling-wave solutions for linear and nonlinear heat-transfer equations

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2307-2311 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang ◽  
Hari Srivastava
Keyword(s):  
Heat Transfer ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Linear Heat ◽  
Wave Solutions ◽  
Nonlinear Heat Transfer ◽  
Transfer Equations ◽  
Non Linear ◽  
Linear And Nonlinear

The exact traveling-wave solutions for the linear and non-linear heat transfer equations at several different excess temperatures are addressed and investigated in this paper.

scholarly journals Explicit Exact Solutions of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Evolution Equation Using the Reliable Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Supaporn Kaewta ◽  
Sekson Sirisubtawee ◽  
Nattawut Khansai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Transformation ◽  
Jacobi Elliptic Function ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Wave Solutions

In this article, we utilize the G′/G2-expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials (Jaulent and Miodek, 1976; Jaulent, 1976). The equation is converted into a fourth order partial differential equation using a transformation. After applying a traveling wave transformation to the resulting partial differential equation, we obtain an ordinary differential equation which is the main equation to which the both schemes are applied. As a first step, the two methods give us distinguish systems of algebraic equations. The first method provides exact traveling wave solutions including the logarithmic function solutions of trigonometric functions, hyperbolic functions, and polynomial functions. The second approach provides the Jacobi elliptic function solutions depending upon their modulus values. Some of the obtained solutions are graphically characterized by the distinct physical structures such as singular periodic traveling wave solutions and peakons. A comparison between our results and the ones obtained from the previous literature is given. Obtaining the exact solutions of the equation shows the simplicity, efficiency, and reliability of the used methods, which can be applied to other nonlinear partial differential equations taking place in mathematical physics.

scholarly journals The Probabilities of Obtaining Solitary Wave and Other Solutions in the Modified Noguchi Power Line

2021 ◽  
Vol 13 (4) ◽  
pp. 19
Author(s):  
Jean R. Bogning ◽  
Cédric Jeatsa Dongmo ◽  
Clément Tchawoua
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Power Line ◽  
Partial Differential ◽  
Strongly Nonlinear ◽  
Wave Solutions

We use the implicit Bogning function (iB-function) to proceed to a kind of inventory of the possible solutions of the modified nonlinear partial differential equation which characterizes the modified power line of Noguchi. Firstly, we make an inventory of the forms of solutions through a field of possible solutions, then we identify the most probable forms that we set out to look for. The iB-function is used because it summarizes within it several types of different functions depending on the choice of its characteristics and it is easy to handle in the case of strongly nonlinear partial differential equations. In other words, we use the notion of probability to locate, through the characteristic indices of iB-functions, the forms of solitary and traveling wave solutions likely to propagate in the modified Noguchi power line.

Traveling Wave Solutions to the Burgers-αβ Equations

2016 ◽  
Vol 16 (1) ◽  
pp. 147-157 ◽  
Author(s):  
Byungsoo Moon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Burgers Equation ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Decay Condition ◽  
Wave Solutions ◽  
Special Case

AbstractThe Burgers-αβ equation, which was first introduced by Holm and Staley [4], is considered in the special case where ${\nu=0}$ and ${b=3}$. Traveling wave solutions are classified to the Burgers-αβ equation containing four parameters ${b,\alpha,\nu}$, and β, which is a nonintegrable nonlinear partial differential equation that coincides with the usual Burgers equation and viscous b-family of peakon equation, respectively, for two specific choices of the parameter ${\beta=0}$ and ${\beta=1}$. Under the decay condition, it is shown that there are smooth, peaked and cusped traveling wave solutions of the Burgers-αβ equation with ${\nu=0}$ and ${b=3}$ depending on the parameter β. Moreover, all traveling wave solutions without the decay condition are parametrized by the integration constant ${k_{1}\in\mathbb{R}}$. In an appropriate limit ${\beta=1}$, the previously known traveling wave solutions of the Degasperis–Procesi equation are recovered.

On the Exact Traveling Wave Solutions to the van der Waals p-System

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
M. Bilal ◽  
M. Younis ◽  
H. Rezazadeh ◽  
T. A. Sulaiman ◽  
A. Yusuf ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Van Der Waals ◽  
Traveling Wave Solutions ◽  
P System ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250126 ◽  
Author(s):  
FANG YAN ◽  
CUNCAI HUA ◽  
HAIHONG LIU ◽  
ZENGRONG LIU
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Auxiliary Function ◽  
Kp Equation ◽  
Gardner Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kp Equations

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

Bifurcations and Exact Traveling Wave Solutions for a Model of Nonlinear Pulse Propagation in Optical Fibers

2014 ◽  
Vol 24 (06) ◽  
pp. 1450088
Author(s):  
Jibin Li
Keyword(s):  
Optical Fibers ◽  
Traveling Wave ◽  
Pulse Propagation ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Wave System ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Pulse Propagation

In this paper, we consider a model of nonlinear pulse propagation in optical fibers. By investigating the dynamical behavior and bifurcations of solutions of the traveling wave system of PDE, we derive all possible exact explicit traveling wave solutions under different parameter conditions. These results completed the study of traveling wave solutions for the mentioned model posed by [Lenells, 2009].

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