On pulse propagation of soliton wave solutions related to the perturbed Chen–Lee–Liu equation in an optical fiber

Baskonus, Hacı Mehmet; Osman, M. S.; Rehman, Hamood Ur; Ramzan, Muhammad; Tahir, Muhammad; Ashraf, Shagufta

doi:10.1007/s11082-021-03190-6

Cited by 92 publications

(15 citation statements)

References 70 publications

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“…In future studies, the ANNs-LMBM approaches have been used to solve the numerical performance of the nonlinear models [35][36][37][38][39][40][41][42].…”

Section: Results and Simulationsmentioning

confidence: 99%

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Weera¹,

Zamart²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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The motive of these investigations is to provide the importance and significance of the fractional order (FO) derivatives in the nonlinear environmental and economic (NEE) model, i.e., FO-NEE model. The dynamics of the NEE model achieves more precise by using the form of the FO derivative. The investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this study. The composition of the FO-NEE model is classified into three classes, execution cost of control, system competence of industrial elements and a new diagnostics technical exclusion cost. The mathematical FO-NEE system is numerically studied by using the artificial neural networks (ANNs) along with the Levenberg-Marquardt backpropagation method (ANNs-LMBM). Three different cases using the FO derivative have been examined to present the numerical performances of the FO-NEE model. The data is selected to solve the mathematical FO-NEE system is executed as 70% for training and 15% for both testing and certification. The exactness of the proposed ANNs-LMBM is observed through the comparison of the obtained and the Adams-Bashforth-Moulton database results. To ratify the aptitude, validity, constancy, exactness, and competence of the ANNs-LMBM, the numerical replications using the state transitions, regression, correlation, error histograms and mean square error are also described.

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“…In future studies, the ANNs-LMBM approaches have been used to solve the numerical performance of the nonlinear models [35][36][37][38][39][40][41][42].…”

Section: Results and Simulationsmentioning

confidence: 99%

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Weera¹,

Zamart²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

show abstract

“…The method can be considered a promising new solver, which can be applied to solve more complicated nonlinear problems [38][39][40][41][42][43].…”

Section: Discussionmentioning

confidence: 99%

An Intelligence Computational Approach for the Fractional 4D Chaotic Financial Model

Weera¹,

Botmart²,

Chantawat³

et al. 2023

Computers, Materials &Amp; Continua

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The main purpose of the study is to present a numerical approach to investigate the numerical performances of the fractional 4-D chaotic financial system using a stochastic procedure. The stochastic procedures mainly depend on the combination of the artificial neural network (ANNs) along with the Levenberg-Marquardt Backpropagation (LMB) i.e., ANNs-LMB technique. The fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional order α. The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and 1. The data proportion is applied as 73%, 15%, and 12% for training, testing, and certification to solve the chaotic fractional system. The acquired results are verified through the comparison of the reference solution, which indicates the proposed technique is efficient and robust. The 4-D chaotic model is numerically solved by using the ANNs-LMB technique to reduce the mean square error (MSE). To authenticate the exactness, and consistency of the technique, the obtained performances are plotted in the figures of correlation measures, error histograms, and regressions. From these figures, it can be witnessed that the provided technique is effective for solving such models to give some new insight into the physical behavior of the model.

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“…Analytical methods commonly used in the literature are as follows. Exp‐function method, 10 Bernoulli sub‐equation function method, 11 F‐expansion method, 12 energy balance method, 13 the direct mapping method, 14

(1 / G^{'})

‐expansion method, 15 and so on 16–29 …”

Section: Introductionmentioning

confidence: 99%

“…Exp-function method, 10 Bernoulli sub-equation function method, 11 F-expansion method, 12 energy balance method, 13 the direct mapping method, 14 1=G 0 À Á -expansion method, 15 and so on. [16][17][18][19][20][21][22][23][24][25][26][27][28][29] We considered the coupled Higgs field equation (CHFE), which is important in nucleus theory. 30 u tt À u xx À αu þ βjuj 2 u À 2uv ¼ 0,…”

Section: Introductionmentioning

confidence: 99%

Traveling wave and general form solutions for the coupled Higgs system

Duran

Durur

Yokuş

2023

Math Methods in App Sciences

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In this study, the coupled Higgs system, which is a special case of the coupled Higgs field equation, which is effective in energy transport in the sub-particles of the atom, is discussed. With the help of the modified generalized exponential rational function method, which is an important instrument in obtaining traveling wave solutions, both the propagating wave solutions and general form solutions of coupled Higgs system are presented. These solutions are examined under some restrictive conditions as they are presented. It is argued that these solutions differ from the literature. The advantages and disadvantages of the method discussed in the conclusion and discussion section are discussed. In addition, the changes in the behavior of the traveling wave solution are discussed by giving physical meaning to some constants in the traveling wave solutions produced by the method. The effects on the traveling wave solution are analyzed for different values of wave number, wave velocity, and wave frequency, which have physically important meanings. In addition, the behaviors caused by these effects are supported with the help of simulation.

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On pulse propagation of soliton wave solutions related to the perturbed Chen–Lee–Liu equation in an optical fiber

Cited by 92 publications

References 70 publications

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

An Intelligence Computational Approach for the Fractional 4D Chaotic Financial Model

Traveling wave and general form solutions for the coupled Higgs system

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