Optical solitons for the perturbed Biswas-Milovic equation with Kudryashov's law of refractive index by the unified auxiliary equation method

Zayed, Elsayed M.E.; Gepreel, Khaled A.; Shohib, Reham M.A.; Alngar, Mohamed E.M.; Yıldırım, Yakup

doi:10.1016/j.ijleo.2021.166286

Cited by 69 publications

(13 citation statements)

References 28 publications

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“…Zayed et al in [35] applied the modified Kudryashov's approach and the addendum to Kudryashov's approach to obtained optical soliton solutions to the cubic-quartic perturbation with Biswas-Milovic equation including Kudryashov's https://www.journals.vu.lt/nonlinear-analysis law of refractive index. This present study further complements and presents new solutions to this nonlinear problem, some of which do not exist in [34,35] before. The structure of this article is as follows: the mathematical formulation of soliton solutions to NLBM equation incorporated with Kudryashov's in polarization preserving fibers and nonlinear perturbation terms along with the application of three novel techniques, the simple equation method, the (G /G)-expansion method, and the new Kudryashov method are detailed in Section 2.…”

Section: Introductionsupporting

confidence: 59%

“…where C is a complex plane, while R 2 is a two-dimensional linear space. The critical concept of this paper is to establish the soliton solutions of NLBM equation incorporated with Kudryashov's in polarization preserving fibers and nonlinear perturbation terms given as [34] i…”

Section: Introductionmentioning

confidence: 99%

“…To achieve this aim, we employed three efficient and reliable schemes, explicitly, the simple equation method, the (G /G)-expansion method, and the new Kudryashov method. Recently, Zayed et al in [34] studied this model with unified auxiliary equation method. Zayed et al in [35] applied the modified Kudryashov's approach and the addendum to Kudryashov's approach to obtained optical soliton solutions to the cubic-quartic perturbation with Biswas-Milovic equation including Kudryashov's https://www.journals.vu.lt/nonlinear-analysis law of refractive index.…”

Section: Introductionmentioning

confidence: 99%

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Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

Akinyemi

Mirzazadeh

Hosseini

2022

NAMC

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We analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, which describes the propagation of pulses of various types in optical fiber. We apply three efficient and reliable schemes, specifically, the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. These approaches lead to a range of solitons and other solutions comprising of the bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions. These solutions are also presented graphically. Furthermore, all obtained solutions are verified by symbolic computations.

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Section: Introductionsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

Akinyemi

Mirzazadeh

Hosseini

2022

NAMC

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“…used toobtain exact solitonsolutions for non-linear partial differential equations, [30] variational iteration method [31], extended exponential function method [32], Hirota bilinear technique [33], power series method [34], F-expansion technique [35] as well as several others [36][37][38][39][40][41][42].…”

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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“…The Biswas-Milovic equation is a special form of the nonlinear Schrödinger equation (NLSE). In polarization-preserving fibers without nonlinear perturbation terms, the nonlinear Biswas-Milovic equation is given by [32,33]…”

Section: Introductionmentioning

confidence: 99%

Study on dynamic features and traveling wave solutions of perturbed nonlinear Biswas–Milovic equation combining Kudryashov's law of refractive index

Li,

2023

Math Methods in App Sciences

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This article mainly explores the Biswas–Milovic equation containing Kudryashov's refractive index law and nonlinear perturbation terms. We take the complete discrimination system for polynomial method and the trial equation method to implement qualitative and quantitative studies for the equation. We verify that the Hamiltonian of the dynamic system is conserved and apply the complete discrimination system of polynomial method to give the associated global phase diagrams, which are qualitatively analyzed to illustrate the presence of periodic solutions and solitons. In addition, we gain a classification of all single traveling wave solutions, provide optical wave patterns with specific parameters and validate the above findings.

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Optical solitons for the perturbed Biswas-Milovic equation with Kudryashov's law of refractive index by the unified auxiliary equation method

Cited by 69 publications

References 28 publications

Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

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

Study on dynamic features and traveling wave solutions of perturbed nonlinear Biswas–Milovic equation combining Kudryashov's law of refractive index

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