Implementation of optical soliton behavior of the space–time conformable fractional Vakhnenko–Parkes equation and its modified model

Mabrouk, S. M.; Rezazadeh, Hadi; Ahmad, Hijaz; Rashed, A. S.; Demirbilek, Ulviye; Gepreel, Khaled A.

doi:10.1007/s11082-023-05553-7

Cited by 8 publications

(2 citation statements)

References 84 publications

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“…The fractional coupled nonlinear Helmholtz (FCNH) equation is presented aswhere ∂cω/∂tα and ∂cϑ/∂xα are conformable derivative (Sahoo and Ray, 2019; Wang, 2023; Akar et al. , 2023; Mabrouk et al. , 2024), and are defined as…”

Section: Introductionmentioning

confidence: 99%

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New computational approaches to the fractional coupled nonlinear Helmholtz equation

Wang

2024

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PurposeThe main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.Design/methodology/approachThis article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.FindingsThe proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.Originality/valueThe fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.

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Section: Introductionmentioning

confidence: 99%

“…where v c ω=vt α and v c ϑ=vx α are conformable derivative (Sahoo and Ray, 2019;Wang, 2023;Akar et al, 2023;Mabrouk et al, 2024), and are defined as…”

Section: Introductionmentioning

confidence: 99%

New computational approaches to the fractional coupled nonlinear Helmholtz equation

Wang

2024

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Solitary wave dynamics of the extended (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff equation

Sadaf,

Arshed,

Akram

et al. 2024

Opt Quant Electron

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Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

Kırcı,

Koç,

Bulut

2024

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This work searches the new wave solutions of the time-fractional ion sound and Langmuir waves (ISLWs) equation and the time-fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation with the conformable derivative. The $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method is employed for these models for the first time. Getting support from symbolic software, some new solutions are presented, which will be constructive for studies in the field of nonlinear physical phenomena. New wave solutions obtained by using the $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method have applications in engineering, physics, and other scientific fields. The regarded method may provide a framework for the exact solutions of several evolution equations in applied sciences. Moreover, the graphical illustrations are also demonstrated to observe the dynamical behaviours of the solutions, which may benefit the development of new technologies.

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Implementation of optical soliton behavior of the space–time conformable fractional Vakhnenko–Parkes equation and its modified model

Cited by 8 publications

References 84 publications

New computational approaches to the fractional coupled nonlinear Helmholtz equation

New computational approaches to the fractional coupled nonlinear Helmholtz equation

Solitary wave dynamics of the extended (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff equation

Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

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