On the application of the double integral method with quadratic temperature profile for spherical solidification of lead and tin metals

Canzian, E.P.; Santiago, Fabio; Lopes, Alisson Vinicius Brito; Barbosa, M.R.; Barañano, Audrei Giménez

doi:10.1016/j.applthermaleng.2022.119528

Cited by 3 publications

(1 citation statement)

References 40 publications

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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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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

View full text Add to dashboard Cite

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Exploring of soliton solutions in optical metamaterials with parabolic law of nonlinearity

Shakeel,

Liu,

Mostafa

et al. 2024

Opt Quant Electron

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Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn

Shakeel,

Abbas,

Rehman

et al. 2024

Sci Rep

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The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. The obtained solutions manifest in various forms including dark, bright, kink, anti-kink, and periodic types using diverse strategies. To enhance the physical interpretation, the study presents 3D, 2D, and contour plots of the acquired solutions. Every graph’s wave-like structure contains information about the structural behaviour of the bacteria that build biofilms on surfaces where rectangles have different densities. This analysis enhances comprehension of the complex dynamics present in areas like fluid dynamics, fiber optics, biology, ocean physics, coastal engineering, and nonlinear complex physical systems.

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On the application of the double integral method with quadratic temperature profile for spherical solidification of lead and tin metals

Cited by 3 publications

References 40 publications

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

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

Exploring of soliton solutions in optical metamaterials with parabolic law of nonlinearity

Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn

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