Nonlinear dispersion in parabolic law medium and its optical solitons

Akinyemi, Lanre; Rezazadeh, Hadi; Yao, Shao-Wen; Akbar, M. Ali; Khater, Mostafa M. A.; Jhangeer, Adil; Ahmad, Harith

doi:10.1016/j.rinp.2021.104411

Cited by 101 publications

(10 citation statements)

References 47 publications

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“…It is an empirical loss minimization algorithm based on the softmax model and uses multiple cross-entropy as objective function. Given a set of training data: S = x (1) , y (1) , x (2) , y (2)…”

Section: Multi-classification Problemmentioning

confidence: 99%

“…Encouraged by the earlier studies, some innovative analytical methods have been proposed. By a set of constraint conditions, the generalized auxiliary equation method is employed to achieve many new exact solutions which are the hyperbolic trigonometric, trigonometric, exponential, and rational [1]. The generalized Kudryashov method is proven to be reliable, efficient, and realistic, and is well suited for accurate isolated wave solution extraction for the Boussinesq model [2].…”

Section: Introductionmentioning

confidence: 99%

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Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

Cheng¹,

Yin²,

Chen³

2022

Computer Modeling in Engineering &Amp; Sciences

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This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods. A model based on the neural network multi-classification algorithm is constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy. The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected. The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model, and the accuracy of the model is about 90%. Finally, by incorporating the predicted Gaussian quadrature points into the boundary element analysis, we find that the numerical solution and the analytical solution are in good agreement, which verifies the robustness of the proposed method.

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Section: Multi-classification Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

Cheng¹,

Yin²,

Chen³

2022

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…In recent years, various types of closed-form solutions of (NLEEs), such as soliton, rational, coupon, periodic and quasi-periodic solutions, have been reported. Non-linear PDEs have a very vast range of practical applications inthe field of wave theory,including transportation of heat and mass,plasma physics, and hydrodynamics chemical technology [14,15], ocean waves process may be characterized by non-linear ordinary differential equation systems [16,17], population ecology [18], electromagnetic wave interaction in a plasma [19], non-linear may appear in quantum mechanics in several different ways [20,21] and so on.…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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“…In light of this, we mention some of the analytical methods in the literature, such as the Jacobi elliptic functions method [15], the exponential expansion method [16], the tanh-based expansion methods [17], the Kudryashov method [18], the G'/G-expansion method [19], the sub-equation method [20] and the modified exponential rational method [21]. For more on analytical methods, see [22][23][24][25][26][27][28]. Furthermore, we mention some of the well-known computational methods for approximate soliton solutions here, including the famous Adomian decomposition approach [29], the Laplace-homotopy perturbation method [30] and the homotopy analysis approach [31], among others.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Nonlinear Modified Benjamin-Bona-Mahony Equation by an Analytical Method

Alotaibi

Althobaiti

2022

Fractal Fract

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The current manuscript investigates the exact solutions of the modified Benjamin-Bona-Mahony (BBM) equation. Due to its efficiency and simplicity, the modified auxiliary equation method is adopted to solve the problem under consideration. As a result, a variety of the exact wave solutions of the modified BBM equation are obtained. Furthermore, the findings of the current study remain strong since Jacobi function solutions generate hyperbolic function solutions and trigonometric function solutions, as liming cases of interest. Some of the obtained solutions are illustrated graphically using appropriate values for the parameters.

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Nonlinear dispersion in parabolic law medium and its optical solitons

Cited by 101 publications

References 47 publications

Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Exact Solutions of the Nonlinear Modified Benjamin-Bona-Mahony Equation by an Analytical Method

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