Optical soliton wave solutions to the resonant Davey–Stewartson system

Aghdaei, Mehdi Fazli; Manafian, Jalil

doi:10.1007/s11082-016-0681-0

Cited by 31 publications

(7 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Manafan et al proposed a new method to solve nonlinear partial diferential equations, namely, the improved tan (φ/2) expansion method [49]. With the help of this method, many classical nonlinear partial diferential equations have been investigated and abundant exact solutions have been obtained [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69]. Mohyud-Din and Irshad used this method to construct an exact solution for the generalised KP equation and explained that it can provide better help for the study of generalised KP equations [60].…”

Section: Introductionmentioning

confidence: 99%

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

renmandula

Yin

2023

Journal of Mathematics

View full text Add to dashboard Cite

In this paper, an improved tan (φ/2) expansion method is used to solve the exact solution of the nonlinear forced (2 + 1)-dimensional Zakharov–Kuznetsov equation. Firstly, we analyse the research status of the improved tan (φ/2) expansion method. Then, exact solutions of the nonlinear forced (2 + 1)-dimensional Zakharov–Kuznetsov equation are obtained by the perturbation expansion method and the multi-spatiotemporal scale method. It is shown that the improved tan (φ/2) expansion method can obtain more exact solutions, including exact periodic travelling wave solutions, exact solitary wave solutions, and singular kink travelling wave solutions. Finally, the three-dimensional figure and the corresponding plane figure of the corresponding solution are given by using MATLAB to illustrate the influence of external source, dimension variable y, and dispersion coefficient on the propagation of the Rossby wave.

show abstract

Section: Introductionmentioning

confidence: 99%

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

renmandula

Yin

2023

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…In addition, we establish singular and dark soliton solutions in terms of trigonometric and hyperbolic, respectively. We consider the CCRDS system in the form [33]:…”

Section: Introductionmentioning

confidence: 99%

New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

Al‐Omari

Alabedalhadi

Al‐Smadi³

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper investigates the novel soliton solutions of the coupled fractional system of the resonant Davey-Stewartson equations. The fractional derivatives are considered in terms of conformable sense. Accordingly, we utilize a complex traveling wave transformation to reduce the proposed system to an integer-order system of ordinary differential equations. The phase portrait and the equilibria of the obtained integer-order ordinary differential system will be studied. Using suitable mathematical assumptions, the new types of bright, singular, and dark soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing system. To achieve this, illustrative examples of the fractional Davey-Stewartson system are provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of conformable derivatives on behavior of acquired solutions for different fractional orders is also discussed. By comparing the proposed method with the other existing methods, the results show that the execute of this method is concise, simple, and straightforward. The results are useful for obtaining and explaining some new soliton phenomena.

show abstract

“…It is also very important to discuss the characteristics of models that occur in ocean dynamics due to the key positions they perform in our day-to-day operations or activities. Because of the applications and rules that NLODEs carry out in our everyday lives, researchers around the world have used a variety of numerical and analytical methods to explore their behaviors, such as the Adomian decomposition method [1][2][3], a semi-implicit method and a finite element method [4], the finite difference method [5,6], a shooting method [7][8][9], a homotopy perturbation method [10], a modified expansion method [11][12][13], the sinh-Gordon expansion method [14][15][16], the sin-Gordon expansion method [17][18][19], an improved tan ( ( ) ) f x 2 [20][21][22], an inverse mapping method [23], the Bäcklund transformation [24], a functional variable method [25], a ( ( )) + ¢ m G G -expansion method [26,27], a modified auxiliary expansion method [28], the Jacobi elliptic function method [29,30], the improved Bernoulli sub-equation function method [31,32], the Riccati-Bernoulli sub-ODE method [33,34], a ( ) ¢ G 1 -expansion method [35,36], and many other numerical and exact techniques [37][38][39][40]…”

Section: Introductionmentioning

confidence: 99%

Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Ismael

Baskonus

Gao

2020

Commun. Theor. Phys.

View full text Add to dashboard Cite

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM. Also, numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement. Besides, the instability modulation of the governing equations are explored through the linear stability analysis function. All new solutions satisfy the main coupled equation after they have been put into the governing equations.

show abstract

Optical soliton wave solutions to the resonant Davey–Stewartson system

Cited by 31 publications

References 51 publications

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

Abundance of Exact Solutions of a Nonlinear Forced (2 + 1)-Dimensional Zakharov–Kuznetsov Equation for Rossby Waves

New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Contact Info

Product

Resources

About