Analytical study of nonlinear water wave equations for their fractional solution structures

Zafar, Asim; İnç, Mustafa; Shakeel, Muhammad; Mohsin, Muhammad

doi:10.1142/s0217984922500713

Cited by 12 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently many powerful techniques for attaining the exact solution of NPDEs have been presented, such as Jacobi-elliptic approach 7 , Sine-Gordon expansion scheme 8 – 10 , modified simple equation scheme 11 , the Kudryashov approach 12 , auxiliary equation technique 13 , 14 , Exp-function method 15 , the extended direct algebraic method 16 – 19 , -expansion method 17 , 20 , extended tanh expansion scheme 21 , -expansion method 22 , Hirota bilinear method 23 , 24 , modified rational expansion method 25 , modified Sardar sub-equation method 26 , the Riccati equation mapping method 27 , F-expansion method 28 and many more 29 – 33 .…”

Section: Introductionmentioning

confidence: 99%

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Shakeel,

Zafar,

Alameri

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified $$\left( \frac{G^{'}}{G^2}\right)$$ G ′ G 2 -expansion method, $$\left( \frac{1}{G^{'}}\right)$$ 1 G ′ -expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of $$\beta$$ β . In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models.

show abstract

Section: Introductionmentioning

confidence: 99%

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Shakeel,

Zafar,

Alameri

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…In recent few decades, many efficient methods or techniques have been used to find the analytical solutions for nonlinear models, such as the Ricatti approach 21 , the Kudryashov method 22 , the Darboux transformation 23 , the Jacobi elliptic function approach 24 , the sine-cosine approach 25 , the direct algebraic technique 26 , the extended tanh function method 27 – 31 , sine-Gordon approach 32 , 33 , Fokas technique 34 , the Hirota bilinear transformation approach 35 , 36 , the first integral approach 37 , the trial solution technique 38 , the -expansion approach 39 , -expansion technique 40 , -expansion technique 41 – 43 , Lie Symmetry method 44 , the unified method 45 , and so on. The travelling wave solution of DSW was attained by utilizing the auxiliary equation method 46 .…”

Section: Introductionmentioning

confidence: 99%

Construction of diverse water wave structures for coupled nonlinear fractional Drinfel’d-Sokolov-Wilson model with Beta derivative and its modulus instability

Shakeel,

AlQahtani,

Rehman

et al. 2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

This paper aims to analyze the coupled nonlinear fractional Drinfel’d-Sokolov-Wilson (FDSW) model with beta derivative. The nonlinear FDSW equation plays an important role in describing dispersive water wave structures in mathematical physics and engineering, which is used to describe nonlinear surface gravity waves propagating over horizontal sea bed. We have applied the travelling wave transformation that converts the FDSW model to nonlinear ordinary differential equations. After that, we applied the generalized rational exponential function method (GERFM). Diverse types of soliton solution structures in the form of singular bright, periodic, dark, bell-shaped and trigonometric functions are attained via the proposed method. By selecting a suitable parametric value, the 3D, 2D and contour plots for some solutions are also displayed to visualize their nature in a better way. The modulation instability for the model is also discussed. The results show that the presented method is simple and powerful to get a novel soliton solution for nonlinear PDEs.

show abstract

Dynamical study of a time fractional nonlinear Schrödinger model in optical fibers

Shakeel,

Bibi,

AlQahtani

et al. 2023

Opt Quant Electron

View full text Add to dashboard Cite

Analytical study of nonlinear water wave equations for their fractional solution structures

Cited by 12 publications

References 34 publications

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation

Construction of diverse water wave structures for coupled nonlinear fractional Drinfel’d-Sokolov-Wilson model with Beta derivative and its modulus instability

Dynamical study of a time fractional nonlinear Schrödinger model in optical fibers

Contact Info

Product

Resources

About