Optical Solitons of Two Non-linear Models in Birefringent Fibres Using Extended Direct Algebraic Method

Rehman, Hamood Ur; Ullah, Naeem; Imran, Muhammad; Akgül, Ali

doi:10.1007/s40819-021-01180-6

Cited by 16 publications

(2 citation statements)

References 50 publications

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“…This challenge persists despite the extensive literature dedicated to constructing exact traveling wave and soliton solutions [6]- [57], [66][67][68][69][70]. In efforts to circumvent these constraints, several scholars have attempted to solve coupled equations by reducing them into single equations through the imposition of drastic constraints [58][59][60][61][62][63][64][65] (to cite just a few). However, such an approach inadvertently alters the original nature of the problem and the underlying physical phenomena these coupled equations represent.…”

Section: Introductionmentioning

confidence: 99%

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Yomba

2024

Phys. Scr.

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Numerous methodologies employed for the exploration of soliton solutions within nonlinear models demonstrate considerable efficacy and efficiency in addressing individual non- linear partial differential equations (NLPDEs). However, their efficacy diminishes when applied to interconnected NLPDEs, owing to the presence of interaction terms in the coupled equations. Consequently, deriving exact solutions for such coupled equations presents a formidable challenge. In response to this challenge, several researchers have endeavored to solve coupled equations by assuming a proportional relationship between the solution in one line and that in another line, resulting in the imposition of excessive constraints and the subsequent reduction of coupled equations to a single equation. Regrettably, this approach compromises the fidelity of the physical phenomena that these equations aim to describe. In contrast, we propose a method characterized by its simplicity and directness, providing a more authentic and insightful analytical perspective for the investigation of coupled NLPDEs. The innovation lies in its capability to simultaneously propagate different types of solitons in two lines with a single operation, while also enabling the natural emergence of analogous solitons in both systems under minimal constraints. We apply this method to scrutinize the propagation of a diverse range of novel coupled progressive solitons in magneto-optical waveguides featuring a parabolic-nonlocal law of nonlinearity and governed by coupled nonlinear Schr ̈odinger equations. The resultant solitons, depicted through detailed 2D and 3D visualizations in Figures 1-12 demonstrate a multitude of coupled soliton forms, several of which are novel in the field.

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Section: Introductionmentioning

confidence: 99%

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Yomba

2024

Phys. Scr.

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“…Therefore, we need different and new techniques to solve such kinds of NLEEs. For this aspect, researchers have developed different, unique, and powerful techniques to solve NLEEs, which include the modified simple equation technique [13][14][15], the variational iteration method [16,17], the variational method [18], the first integral method [19], the perturbation method [20], method of integrability [21], the nonperturbative technique [22], the modified F-expansion method [23][24][25], the exp-function method [26,27], the sine-cosine method [28][29][30], the Riccatti-Bernoulli sub-ODE method [31,32], the Jacobi elliptic function method [33,34], the generalized Kudryashov method [35,36], the functional variable method [37,38], the modified Khater method [39,40], the new extended direct algebraic method [41,42], the Lie symmetry technique [43,44], the (G /G)-expansion method [45], the tanh-coth method [46,47], the new auxiliary equation method [48,49], the (G /G, 1/G)expansion method [50], the technique of (m + 1, G ) [51], the addendum to Kudryashov's method [52], and many others [53]…”

Section: Introductionmentioning

confidence: 99%

Diverse Variety of Exact Solutions for Nonlinear Gilson–Pickering Equation

et al. 2022

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The purpose of this article is to achieve new soliton solutions of the Gilson–Pickering equation (GPE) with the assistance of Sardar’s subequation method (SSM) and Jacobi elliptic function method (JEFM). The applications of the GPE is wider because we study some valuable and vital equations such as Fornberg–Whitham equation (FWE), Rosenau–Hyman equation (RHE) and Fuchssteiner–Fokas–Camassa–Holm equation (FFCHE) obtained by particular choices of parameters involved in the GPE. Many techniques are available to convert PDEs into ODEs for extracting wave solutions. Most of these techniques are a case of symmetry reduction, known as nonclassical symmetry. In our work, this approach is used to convert a PDE to an ODE and obtain the exact solutions of the NLPDE. The solutions obtained are unique, remarkable, and significant for readers. Mathematica 11 software is used to derive the solutions of the presented model. Moreover, the diagrams of the acquired solutions for distinct values of parameters were demonstrated in two and three dimensions along with contour plots.

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Exploring localized waves and different dynamics of solitons in (2 + 1)-dimensional Hirota bilinear equation: a multivariate generalized exponential rational integral function approach

Niwas,

Kumar,

Rajput

et al. 2024

Nonlinear Dyn

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Optical Solitons of Two Non-linear Models in Birefringent Fibres Using Extended Direct Algebraic Method

Cited by 16 publications

References 50 publications

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Diverse Variety of Exact Solutions for Nonlinear Gilson–Pickering Equation

Exploring localized waves and different dynamics of solitons in (2 + 1)-dimensional Hirota bilinear equation: a multivariate generalized exponential rational integral function approach

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