scholarly journals New Application of the(G′/G)-Expansion Method for Thin Film Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wafaa M. Taha ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Closed Form Solution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Form Solution ◽  
Thin Film Equations ◽  
First Time ◽  
Positive Integers ◽  
Good Agreement

The(G′/G)-expansion method is used for the first time to find traveling wave solutions for thin film equations, where it is found that the related balance numbers are not the usual positive integers. The closed-form solution obtained via this method is in good agreement with the previously obtained solutions of other researchers. It is also noted that, for appropriate parameters, new solitary waves solutions are found.

Traveling-wave solutions to thin-film equations

1993 ◽  
Vol 48 (6) ◽  
pp. 4423-4431 ◽  
Author(s):  
Stefanella Boatto ◽  
Leo P. Kadanoff ◽  
Piero Olla
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Thin Film Equations

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals A Theoretical Study on an Elastic Polymer Thin Film-Based Capacitive Wind-Pressure Sensor

Polymers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2133
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Bin-Bin Shi ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He
Keyword(s):  
Thin Film ◽  
Closed Form ◽  
Pressure Sensor ◽  
Closed Form Solution ◽  
Form Solution ◽  
Wind Pressure ◽  
Polymer Thin Film ◽  
Movable Electrode ◽  
Elastic Polymer ◽  
Electrode Plate

This study is devoted to the design of an elastic polymer thin film-based capacitive wind-pressure sensor to meet the anticipated use for real-time monitoring of structural wind pressure in civil engineering. This sensor is composed of four basic units: lateral elastic deflection unit of a wind-driven circular polymer thin film, parallel plate capacitor with a movable circular electrode plate, spring-driven return unit of the movable electrode plate, and dielectric materials between electrode plates. The capacitance of the capacitor varies with the parallel move of the movable electrode plate which is first driven by the lateral elastic deflection of the wind-driven film and then is, after the wind pressure is reduced or eliminated, returned quickly by the drive springs. The closed-form solution for the contact problem between the wind-driven thin film and the spring-driven movable electrode plate is presented, and its reliability is proved by the experiment conducted. The numerical examples conducted show that it is workable that by using the numerical calibration based on the presented closed-form solution the proposed sensor is designed into a nonlinear sensor with larger pressure-monitoring range and faster response speed than the linear sensor usually based on experimental calibration.

scholarly journals Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (G′/G)-Expansion Method

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Expansion Method ◽  
Reaction Diffusion Equation ◽  
Wave Solutions ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation ◽  
Constant Coefficients

We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.

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