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.

Dispersive soliton solutions for the Salerno equation for the nonlinear discrete electrical lattice in the forbidden bandgaps

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional ◽  
Bright Solitons ◽  
Jacobi Elliptic Function Method

In this paper, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear discrete electrical lattice in the forbidden bandgaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, three-dimensional and two-dimensional graphs are presented.

scholarly journals New Soliton Solutions of The Nonlinear Radhakrishnan-Kundu-Lakshmanan Equation With the Beta-Derivative

2021 ◽  
Author(s):  
Yusuf Pandir ◽  
Yusuf Gurefe ◽  
Tolga Akturk
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Two Dimensional ◽  
New Exact Solutions ◽  
Definition Of ◽  
Exponential Function Method

Abstract In this article, the modified exponential function method is applied to find the exact solutions of the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. The definition of the conformable beta derivative and its properties proposed by Atangana are given. With the proposed method, exact solutions of the nonlinear Radhakrishnan-Kundu-Lakshmanan equation which can be stated with the conformable beta-derivative of Atangana are obtained. The exact solutions found as a result of the application of the method seem to be 1-soliton solutions, dark soliton solutions, periodic soliton solutions and rational function solutions. According to the obtained results, we can say that the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative have different soliton solutions. Also, three-dimensional contour and density graphs and two- dimensional graphs drawn with different parameters are given of these new exact solutions.

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.

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.

scholarly journals Construction of Solitary Two-Wave Solutions for a New Two-Mode Version of the Zakharov-Kuznetsov Equation

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1127 ◽  
Author(s):  
Imad Jaradat ◽  
Marwan Alquran
Keyword(s):  
Phase Velocity ◽  
Exact Solutions ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
Velocity Parameter ◽  
Interaction Dynamics ◽  
Wave Solutions ◽  
Proposed Model ◽  
Singular Soliton

A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity parameter. Three different methods are used to obtain exact bell-shaped soliton solutions and singular soliton solutions to the proposed model. Two-dimensional and three-dimensional plots are also provided to illustrate the interaction dynamics of the obtained two-wave exact solutions upon increasing the phase-velocity parameter.

scholarly journals Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Bo Tang ◽  
Xuemin Wang ◽  
Yingzhe Fan ◽  
Junfeng Qu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Mathematical Tool ◽  
Auxiliary Equation Method

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of variable-coefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for the KdV-MKdV equation are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving many other nonlinear partial differential equations with variable coefficients in mathematical physics.

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.

scholarly journals New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Alvaro H. Salas ◽  
Lorenzo J. Martinez H ◽  
David L. Ocampo R
Keyword(s):  
Elliptic Function ◽  
Function Method ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Jacobi Elliptic Function ◽  
Series Method ◽  
Power Series Method ◽  
Weierstrass Elliptic Function ◽  
Generalized Bbm Equation ◽  
Bbm Equation

The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.

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