Investigation of adequate closed form travelling wave solution to the space-time fractional non-linear evolution equations

Arefin, Mohammad Asif; Khatun, M. Ayesha; Uddin, M. Hafiz

doi:10.1016/j.joes.2021.08.011

Cited by 29 publications

(5 citation statements)

References 39 publications

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“…As it can be noted, both the 3D plots in Figure 4 and Figure 6 portrayed kink-typed shapes; while in Figure 5 and Figure 7, the evolution of the hyperelastic wave in the media has been captured to be increasing with an increase in the propagating time. Besides, concerned readers can equally read [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] for some of the recent proposed and deployed analytical approaches for the analytical examination of wave propagation in the contemporary nonlinear media.…”

Section: Graphical Depictions and Discussionmentioning

confidence: 99%

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

Althobaiti

2023

Preprint

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The propagation of waves on nonlinear structures is a vital feature that plays a significant part in elastodynamics. Thus, the current study makes use of some powerful analytical approaches to examine the propagation of nonlinear elastic waves on a Murnaghan hyperelastic circular pipe. Indeed, the admittance of double dispersion terms coupled with the presence of material nonlinearity in the governing nonlinear mode is what makes the study superb. Therefore, some interesting exact analytical solutions are constructed and further analyzed with regard to the parameters that characterize the propagation. In the end, some graphical depictions of some of the gained solutions are supplied to for clarification.

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Section: Graphical Depictions and Discussionmentioning

confidence: 99%

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

Althobaiti

2023

Preprint

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“…Numerous strategies for obtaining various soliton solutions to these NLPDEs have been discovered in the literature. Among these are the square operator approach (Wang et al 2022), the unified technique (Vivas-Cortez et al 2023), Hirota's bilinear approach , the neural network approach (Xu et al 2023), the extended tanh-function approach (Zaman et al 2023a, b), and many others (Arefin et al 2022;. They have enhanced the dynamic approach by employing various methods, such as the generalized Kudryashov method (Akbar et al 2022), the sinh-Gordon equation expansion method (Akbar et al 2021), the (G � ∕G)-expansion , the tanh technique (Almusawa et al 2022), the rational (1∕Φ � )-expansion approach ).…”

Section: Introductionmentioning

confidence: 99%

Multi-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation

Ansari,

Jhangeer,

Imran

et al. 2024

Opt Quant Electron

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This manuscript delves into the examination of the stochastic fractional derivative of Drinfel’d-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena.

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“…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

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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.

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Investigation of adequate closed form travelling wave solution to the space-time fractional non-linear evolution equations

Cited by 29 publications

References 39 publications

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

Multi-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation

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

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