scholarly journals Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles

2021 ◽  
pp. 247-247
Author(s):  
Haci Baskonus ◽  
Adnan Mahmud ◽  
Kalsum Abdulrahman Muhamad ◽  
Tanfer Tanriverdi ◽  
Wei Gao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Function Method ◽  
Dynamical Equation ◽  
Nonlinear Partial Differential Equation ◽  
Gas Bubbles ◽  
Partial Differential ◽  
Wave Solutions

In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov nonlinear partial differential equation are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted.

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 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.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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