Chirped optical solitons for Triki–Biswas equation

Rizvi, Syed T. R.; Afzal, Insibat; Ali, Kashif

doi:10.1142/s0217984919502646

Cited by 22 publications

(5 citation statements)

References 17 publications

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“…Numerous studies explored the applications and theoretical foundations of Sobolev PDEs, underscoring their significance in both theoretical and applied contexts. However, numerous researchers faced challenges in deriving and formulating various complex phenomena within nonlinear PDEs with integer orders [9]. In response, fractional calculus is regarded as a viable solution to this issue, as it incorporates a nonlocal property that is absent in nonlinear PDEs with integer orders [10].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

Ahmad,

Alshammari,

Jan

et al. 2024

Fractal Fract

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The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources.

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Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

Ahmad,

Alshammari,

Jan

et al. 2024

Fractal Fract

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show abstract

“…Extensive research has been carried out in the advancement of numerical and analytical solutions of linear and nonlinear FPDEs [1][2][3][4][5][6]. However, several researchers have not succeeded in deriving and modeling many complex phenomena utilizing linear or nonlinear PDEs with integer order [7]. Subsequently, the fractional is taken as account and is a good solution to this problem [8].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Multiterm Time‐Fractional Model for Heat Conductivity by Local Meshless Technique

et al. 2021

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Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-term time-fractional Sobolev model equation using computationally attractive and reliable technique, known as a local meshless method. Because of the meshless character and the simple application in higher dimensions, there is a growing interest in meshless techniques. To assess the reliability and accuracy of the proposed method, three test problems and two types of irregular domains are taken into account.

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“…Besides the significance they bring to the fundamental understanding of soliton physics, soliton molecules also present the possibility of transferring optical data surpassing the limitation of binary coding [9]. The soliton is a universal concept applicable to a large class of solitary wave propagation effects that can be observed in most branches of nonlinear science [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Yang¹,

Fan²,

Li³

2020

Phys. Scr.

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Soliton molecules may exists in both experimental and theotetical aspects. In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. Soliton molecules are generated by N-soliton solution and a new velocity resonance condition. Furthermore, soliton molecules can become to asymmetric solitons when the distance between two solitons of the molecule is small enough. Based on the N-soliton solution, we obtain some novel interaction solutions which component of soliton molecules, breather waves and lump waves by deal with part of parameters by applying velocity resonance, module resonance and long wave limit method, and the interactions are elastic. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.

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Chirped optical solitons for Triki–Biswas equation

Cited by 22 publications

References 17 publications

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

Numerical Solution of the Multiterm Time‐Fractional Model for Heat Conductivity by Local Meshless Technique

Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

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