scholarly journals New Exact Soliton Solutions of the ( 3 + 1 )-Dimensional Conformable Wazwaz–Benjamin–Bona–Mahony Equation via Two Novel Techniques

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Mohammed K. A. Kaabar ◽  
Melike Kaplan ◽  
Zailan Siri
Keyword(s):  
Soliton Solutions ◽  
Graphical Representations ◽  
Conformable Derivative ◽  
Wolfram Mathematica ◽  
Novel Methods ◽  
Exact Soliton Solutions

In this work, the ( 3 + 1 )-dimensional Wazwaz–Benjamin–Bona–Mahony equation is formulated in the sense of conformable derivative. Two novel methods of generalized Kudryashov and exp − φ ℵ are investigated to obtain various exact soliton solutions. All algebraic computations are done with the help of the Maple software. Graphical representations are provided in 3D and 2D profiles to show the behavior and dynamics of all obtained solutions at various parameters’ values and conformable orders using Wolfram Mathematica.

scholarly journals Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

2020 ◽  
Vol 8 ◽  
Author(s):  
Hemen Dutta ◽  
Hatıra Günerhan ◽  
Karmina K. Ali ◽  
Resat Yilmazer
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Non Linear ◽  
Exact Soliton Solutions

AN INTERNET TRAFFIC FLOW MODEL VIA A CONFORMABLE DERIVATIVE: THE EXACT SOLITON SOLUTIONS

2019 ◽  
Vol 21 (2) ◽  
pp. 227-237
Author(s):  
Yussri M. Mahrous ◽  
S. M. Khaled ◽  
Abdelhalim Ebaid
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Soliton Solutions ◽  
Internet Traffic ◽  
Conformable Derivative ◽  
Traffic Flow Model ◽  
Exact Soliton Solutions

scholarly journals Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

AIP Advances ◽  
2014 ◽  
Vol 4 (6) ◽  
pp. 067131 ◽  
Author(s):  
Ying Wang ◽  
Yu Zhou
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Pitaevskii Equation ◽  
Exact Soliton Solutions

Exact soliton solutions for the core of dispersion-managed solitons

2003 ◽  
Vol 68 (4) ◽  
Author(s):  
Zhiyong Xu ◽  
Lu Li ◽  
Zhonghao Li ◽  
Guosheng Zhou ◽  
K. Nakkeeran
Keyword(s):  
Soliton Solutions ◽  
The Core ◽  
Exact Soliton Solutions

On the exact soliton solutions and different wave structures to the double dispersive equation

2022 ◽  
Vol 54 (2) ◽  
Author(s):  
Usman Younas ◽  
Muhammad Bilal ◽  
Tukur Abdulkadir Sulaiman ◽  
Jingli Ren ◽  
Abdullahi Yusuf
Keyword(s):  
Soliton Solutions ◽  
Dispersive Equation ◽  
Exact Soliton Solutions

scholarly journals On the exact and numerical solutions to a nonlinear model arising in mathematical biology

2018 ◽  
Vol 22 ◽  
pp. 01061 ◽  
Author(s):  
Asif Yokus ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Sibel Pasali Atmaca
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Hyperbolic Function ◽  
Von Neumann ◽  
Convection Diffusion Equation ◽  
Wolfram Mathematica ◽  
Forward Difference ◽  
Von Neumann Analysis ◽  
The Stability

This study acquires the exact and numerical approximations of a reaction-convection-diffusion equation arising in mathematical bi- ology namely; Murry equation through its analytical solutions obtained by using a mathematical approach; the modified exp(-Ψ(η))-expansion function method. We successfully obtained the kink-type and singular soliton solutions with the hyperbolic function structure to this equa- tion. We performed the numerical simulations (3D and 2D) of the obtained analytical solutions under suitable values of parameters. We obtained the approximate numerical and exact solutions to this equa- tion by utilizing the finite forward difference scheme by taking one of the obtained analytical solutions into consideration. We investigate the stability of the finite forward difference method with the equation through the Fourier-Von Neumann analysis. We present the L2 and L∞ error norms of the approximations. The numerical and exact approx- imations are compared and the comparison is supported by a graphic plot. All the computations and the graphics plots in this study are car- ried out with help of the Matlab and Wolfram Mathematica softwares. Finally, we submit a comprehensive conclusion to this study.

New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

2021 ◽  
pp. 2150444
Author(s):  
Loubna Ouahid ◽  
M. A. Abdou ◽  
S. Owyed ◽  
Sachin Kumar
Keyword(s):  
Evolution Equations ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Optical Soliton ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Closed Form Solutions ◽  
Special Solutions ◽  
Engineering Physics ◽  
Exact Soliton Solutions

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods’ performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order.

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

2021 ◽  
pp. 2150263
Author(s):  
A. Tripathy ◽  
S. Sahoo ◽  
S. Saha Ray ◽  
M. A. Abdou
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Ode Method ◽  
Novel Methods

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

scholarly journals New soliton solutions of anti-self-dual Yang-Mills equations

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Masashi Hamanaka ◽  
Shan-Chi Huang
Keyword(s):  
Gauge Group ◽  
Darboux Transformation ◽  
Domain Walls ◽  
Soliton Solutions ◽  
Real Space ◽  
Explicit Calculation ◽  
Yang Mills ◽  
Action Density ◽  
New Type ◽  
Exact Soliton Solutions

Abstract We study exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density TrFμνFμν can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group G = U(2) can be realized on our solition solutions or not is also discussed on each real space.

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