scholarly journals Exact solutions to the foam drainage equation by using the new generalized(G′/G)-expansion method

2015 ◽  
Vol 5 ◽  
pp. 168-177 ◽  
Author(s):  
Md. Nur Alam
Keyword(s):  
Exact Solutions ◽  
Expansion Method ◽  
Foam Drainage Equation ◽  
Foam Drainage

MULTIPLE EXACT SOLUTIONS OF THE GENERALIZED TIME FRACTIONAL FOAM DRAINAGE EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050062
Author(s):  
DANDAN SHI ◽  
YUFENG ZHANG ◽  
WENHAO LIU
Keyword(s):  
Exact Solutions ◽  
Expansion Method ◽  
Transformation Method ◽  
Vertical Density Profile ◽  
New Exact Solutions ◽  
Vertical Density ◽  
Foam Drainage Equation ◽  
Physical Phenomena ◽  
Generalized Time ◽  
Foam Drainage

In this paper, we investigate the exact solutions of the generalized time fractional foam drainage equation. The Lie-group scaling transformation method and improved [Formula: see text]-expansion method are adopted here. The equation describes the evolution of the vertical density profile of a foam under gravity. New exact solutions and maple diagrams of the generalized time fractional foam drainage equation can help us better understand the physical phenomena.

Exact solutions for nonlinear foam drainage equation

2016 ◽  
Vol 91 (2) ◽  
pp. 209-218 ◽  
Author(s):  
E. M. E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Exact Solutions ◽  
Foam Drainage Equation ◽  
Foam Drainage

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

Numerical solutions of the fractal foam drainage equation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Siddra Habib ◽  
Asad Islam ◽  
Amreen Batool ◽  
Muhammad Umer Sohail ◽  
Muhammad Nadeem
Keyword(s):  
Numerical Solutions ◽  
Foam Drainage Equation ◽  
Fractal Foam ◽  
Foam Drainage

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

Sign in / Sign up

Export Citation Format

Share Document