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.

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.

scholarly journals On the wave solutions to the TRLW equation

2018 ◽  
Vol 22 ◽  
pp. 01033
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Canan Unlu ◽  
Hasan Bulut
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Models ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
2D And 3D ◽  
Singular Soliton

In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science.

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.

scholarly journals Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+1)-dimensional

2021 ◽  
Vol 11 (1) ◽  
pp. 92-99
Author(s):  
Haci Mehmet Baskonus
Keyword(s):  
Exponential Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Wolfram Mathematica ◽  
Waves Propagation ◽  
Exponential Function Method ◽  
2D And 3D

In this manuscript, new dark and trigonometric function traveling wave soliton solutions to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by using the modified exponential function method are successfully obtained. Along with novel dark structures, trigonometric solutions are also extracted. For deeper investigating of waves propagation on the surface, 2D and 3D graphs along with contour simulations via computational programs such as Wolfram Mathematica, Matlap softwares and so on are presented.

scholarly journals Different soliton solutions to the modified equal-width wave equation with Beta-time fractional derivative via two different methods

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Different Types ◽  
Non Linear ◽  
Time Fractional Derivative

‎In this paper‎, ‎different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as‎: ‎extended Jacobi's elliptic expansion function method and Kudryashov method‎. ‎The dark‎, ‎bright‎, ‎singular and other solitons are achieved‎. ‎The obtained soliton solutions are verified through MATHEMATICA‎. ‎At the end‎, ‎the results are also explained through graphs‎. ‎These soliton solutions suggest that these two methods are effective‎, ‎straight forward and reliable as compare to other methods‎. ‎The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures‎.

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

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