Local M-derivative of order $$\alpha$$ α and the modified expansion function method applied to the longitudinal wave equation in a magneto electro-elastic circular rod

2018 ◽  
Vol 50 (10) ◽  
Author(s):  
H. Yépez-Martínez ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Wave Equation ◽  
Longitudinal Wave ◽  
Function Method

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with M-derivative

2019 ◽  
Vol 33 (21) ◽  
pp. 1950251 ◽  
Author(s):  
H. M. Baskonus ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Wave Equation ◽  
Longitudinal Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
2D And 3D ◽  
Singular Soliton

In this paper, using the Bernoulli sub-equation function method, we obtain new dark, complex and singular soliton solutions for the longitudinal wave equation in a magneto-electro-elastic circular rod with [Formula: see text]-derivative. Many new complex singular soliton solutions are successfully extracted. For better understanding of physical meanings, we plotted 2D and 3D graphs along with contour simulations.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

New Solitary Wave Solution for the Boussinesq Wave Equation Using the Semi-Inverse Method and the Exp-Function Method

2009 ◽  
Vol 64 (11) ◽  
pp. 709-712 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Wave Equation ◽  
Variational Principle ◽  
Solitary Wave ◽  
Wave Solution ◽  
Variational Formulation ◽  
Function Method ◽  
Inverse Method ◽  
Solitary Wave Solution ◽  
Solitary Solutions

Using the semi-inverse method, a variational formulation is established for the Boussinesq wave equation. Based on the obtained variational principle, solitary solutions in the sech-function and expfunction forms are obtained

Abundant exact solutions to the strain wave equation in micro-structured solids

2021 ◽  
pp. 2150439
Author(s):  
Karmina K. Ali ◽  
R. Yilmazer ◽  
H. Bulut ◽  
Tolga Aktürk ◽  
M. S. Osman
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Exact Solutions ◽  
Rational Function ◽  
Physical Interpretation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Singular Solutions ◽  
Strain Wave ◽  
Important Place

In this study, the strain wave equation in micro-structured solids which take an important place in solid physics is presented for consideration. The generalized exponential rational function method is used for this purpose which is one of the most powerful methods of constructing abundantly distinct, exact solutions of nonlinear partial differential equations. In micro-structured solids, wave propagation is based on the structure of the strain wave equation. As a consequence, we successfully received many different exact solutions, including non-topological solutions, periodic singular solutions, topological solutions, singular solutions, like periodic lump solutions. Furthermore, in order to better understand their physical interpretation, 2D, 3D, and counter plots are graphed for each of the solutions acquired.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

2020 ◽  
pp. 2150086 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Mapping Method ◽  
Integration Scheme ◽  
Auxiliary Equation ◽  
New Exact Solutions ◽  
Non Linear ◽  
Physical Phenomena

This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equation with dispersion caused by transverse Poisson’s effect arises in a magneto-electro-elastic (MEE) circular rod. Explicit new exact solutions are derived in different form such as hyperbolic, kinky, anti-kinky, dark, and singular solitons of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena.

A Modified Test Function Method for Damped Wave Equations

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Marcello D’Abbicco ◽  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Critical Exponent ◽  
Function Method ◽  
Wave Equations ◽  
Time Dependent ◽  
Small Data ◽  
Test Function ◽  
Test Function Method ◽  
Modified Test

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

scholarly journals Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelfattah El Achab
Keyword(s):  
Wave Equation ◽  
Elliptic Function ◽  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Generalized Boussinesq Equation

Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

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