Novel soliton solutions of four sets of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations

2021 ◽  
Author(s):  
Lanre Akinyemi ◽  
Mehmet Şenol ◽  
Emad Az-Zo’bi ◽  
P. Veeresha ◽  
Udoh Akpan
Keyword(s):  
Applied Sciences ◽  
Exact Solutions ◽  
Riccati Equation ◽  
Physical Phenomenon ◽  
Soliton Solutions ◽  
Computational Method ◽  
Physical Parameters ◽  
Ocean Engineering ◽  
Dark Solitons ◽  
The Stability

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not exist in the literature have been obtained in the form of trigonometric, hyperbolic, and rational. These solutions are of considerable importance in applied sciences, coastal, and ocean engineering, where the B–KP-like equations modeled for some significant physical phenomenon. The graph of the bright and dark solitons is presented in order to demonstrate the influence of different physical parameters on the solutions. All of the findings prove the stability, effectiveness, and accuracy of the proposed method.

scholarly journals Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alvaro H. Salas S ◽  
Cesar A. Gómez S
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Third Order ◽  
Forcing Term ◽  
Projective Riccati Equation Method

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

scholarly journals The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3995-4000
Author(s):  
Xiao-Jun Yin ◽  
Quan-Sheng Liu ◽  
Lian-Gui Yang ◽  
N Narenmandula
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Electrostatic Potential ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
The Other ◽  
Equation Method ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expan?sion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.

New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method

2021 ◽  
pp. 2150163
Author(s):  
Seyed Mehdi Mirhosseini-Alizamini ◽  
Najib Ullah ◽  
Jamilu Sabi’u ◽  
Hadi Rezazadeh ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Physical Phenomenon ◽  
Ocean Engineering ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Different Types

In this work, we investigate a new Kudryashov method (NKM) to find the exact and some new solutions of four different types of nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). This is an appropriate algorithm for finding the exact solutions and also working for different types of nonlinear confirmable differential equations. In coastal and ocean engineering, some physical phenomenon is based on the exact solutions of the NLACBEs.

scholarly journals Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Cesar A. Gómez S ◽  
Alvaro H. Salas ◽  
Bernardo Acevedo Frias
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Point Of View ◽  
Computational Method ◽  
New Approach ◽  
Wave Solutions ◽  
Projective Riccati Equation Method ◽  
Kdv6 Equation

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.

scholarly journals Stability analysis on dark solitons in quasi-1D Bose–Einstein condensate with three-body interactions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yushan Zhou ◽  
Hongjuan Meng ◽  
Juan Zhang ◽  
Xiaolin Li ◽  
Xueping Ren ◽  
...  
Keyword(s):  
Einstein Condensate ◽  
Physical Parameters ◽  
Stability Properties ◽  
Body Interaction ◽  
Multi Scale ◽  
Dark Solitons ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Three Body ◽  
Bose Einstein

AbstractThe stability properties of dark solitons in quasi-one-dimensional Bose–Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.

scholarly journals Hyperbolic rational solutions to a variety of conformable fractional Boussinesq-Like equations

2019 ◽  
Vol 8 (1) ◽  
pp. 224-230 ◽  
Author(s):  
Hadi Rezazadeh ◽  
M.S. Osman ◽  
Mostafa Eslami ◽  
Mohammad Mirzazadeh ◽  
Qin Zhou ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Rational Function ◽  
Fractional Differential Equations ◽  
Present Method ◽  
Physical Phenomenon ◽  
Ocean Engineering ◽  
Rational Solutions ◽  
Fractional Differential

Abstract The aim of this paper is to investigate hyperbolic rational solutions of four conformable fractional Boussinesq-like equations using the method of exponential rational function (ERF). The present method is a good scheme, reveal distinct exact solutions and convenient for solving other types of nonlinear conformable fractional differential equations. These solutions are of significant importance in coastal and ocean engineering where the fractional Boussinesq-like equations modeled for some special physical phenomenon.

scholarly journals Charge Transfer Complexes of Ketotifen with 2,3-Dichloro-5,6-dicyano-p-benzoquinone and 7,7,8,8-Tetracyanoquodimethane: Spectroscopic Characterization Studies

Molecules ◽  
2021 ◽  
Vol 26 (7) ◽  
pp. 2039
Author(s):  
Gamal A. E. Mostafa ◽  
Ahmed Bakheit ◽  
Najla AlMasoud ◽  
Haitham AlRabiah
Keyword(s):  
Charge Transfer ◽  
Spectroscopic Characterization ◽  
Molar Ratio ◽  
Charge Transfer Complexes ◽  
Physical Parameters ◽  
Spectrophotometric Methods ◽  
Theoretical Approaches ◽  
The Stability ◽  
Ct Complexes

The reactions of ketotifen fumarate (KT) with 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) as π acceptors to form charge transfer (CT) complexes were evaluated in this study. Experimental and theoretical approaches, including density function theory (DFT), were used to obtain the comprehensive, reliable, and accurate structure elucidation of the developed CT complexes. The CT complexes (KT-DDQ and KT-TCNQ) were monitored at 485 and 843 nm, respectively, and the calibration curve ranged from 10 to 100 ppm for KT-DDQ and 2.5 to 40 ppm for KT-TCNQ. The spectrophotometric methods were validated for the determination of KT, and the stability of the CT complexes was assessed by studying the corresponding spectroscopic physical parameters. The molar ratio of KT:DDQ and KT:TCNQ was estimated at 1:1 using Job’s method, which was compatible with the results obtained using the Benesi–Hildebrand equation. Using these complexes, the quantitative determination of KT in its dosage form was successful.

scholarly journals Numerical simulation of periodic MHD casson nanofluid flow through porous stretching sheet

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdullah Al-Mamun ◽  
S. M. Arifuzzaman ◽  
Sk. Reza-E-Rabbi ◽  
Umme Sara Alam ◽  
Saiful Islam ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Lewis Number ◽  
Stability And Convergence ◽  
Radiation Absorption ◽  
Physical Parameters ◽  
Theoretical Idea ◽  
Prostate Cancer Therapy ◽  
Flow Through ◽  
Explicit Finite Difference ◽  
The Stability

AbstractThe perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, Pr ≥ 0.447 indicates the value of Prandtl number and Le ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.

Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects

2012 ◽  
Vol 67 (6-7) ◽  
pp. 338-346
Author(s):  
Chao-Qing Dai ◽  
Hai-Ping Zhu ◽  
Chun-Long Zheng
Keyword(s):  
Optical Fibers ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Order Effects ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Tunnelling Effect ◽  
Tunnelling Effects ◽  
Higher Order Effects

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

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.

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