Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

Wang, Xin; Zhang, Lingling; Essel, John Fiifi

doi:10.1002/mma.8047

Cited by 7 publications

(4 citation statements)

References 55 publications

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“…The transmission of femtosecond optical pulses in single-mode fiber can be described by HNLSE, which also characterizes various physical effects in single-mode fiber [32]. Describing the impact of these physical effects on soliton transmission can deepen our understanding of the formation of solitons in optical fiber and provide theoretical guidance for realizing high-capacity, long-distance femtosecond soliton communication, and it has the form…”

Section: Physical Model and Scpinn Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Fang¹,

Bo²,

Wang³

et al. 2022

Chaos, Solitons & Fractals

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Section: Physical Model and Scpinn Methodsmentioning

confidence: 99%

“…model is derived from the classical NLSE by using the multi-scale method [32], and it is mainly used to describe the real physical situation of femtosecond optical pulse transmission in optical fibers. The real and imaginary parts of Eq.…”

mentioning

confidence: 99%

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Fang¹,

Bo²,

Wang³

et al. 2022

Chaos, Solitons & Fractals

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“…For more details about the properties of fractional derivatives, see [50,51]. The FDE (9.1) is useful to investigate the anomalous diffusion mechanism commonly involved in transport processes through disordered systems including fractal media [52,53]. In [54], the diffusion equation was used to model the spatiotemporal dynamics of a tumor, taking into account the heterogeneity of the medium.…”

Section: Applicationsmentioning

confidence: 99%

A family of iterative methods to solve nonlinear problems with applications in fractional differential equations

Erfanifar,

Hajarian,

Sayevand

2023

Math Methods in App Sciences

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In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations. The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into memory methods, their efficiency indices are increased. Then, the methods are extended to the multi‐step methods for finding the solutions to systems of problems. The formula for the order of convergence of the multi‐step iterative methods is , where is the step number of the methods. It is clear that computing the Jacobian matrix derivative evaluation and its inversion are expensive; therefore, we compute them only once in every cycle of the methods. The important feature of these multi‐step methods is their high‐efficiency index. Numerical examples that confirm the theoretical results are performed. In applications, some nonlinear problems related to the numerical approximation of fractional differential equations (FDEs) are constructed and solved by the proposed methods.

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“…Therefore, finding analytical solutions for NLEEs increase is significant nowadays. The nonlinear Schrödinger equation (NLSE) is one of the most paramount NLEEs encountered in the study of nonlinear optics [1][2][3][4][5][6][7]. The NLSE is a universal prototype that depicts many physical nonlinear systems.…”

mentioning

confidence: 99%

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

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This work concerns the fractional‐order dual‐mode nonlinear Schrödinger equation (FDMNLSE), which portrays the augmentation or absorption of dual waves. This model dissects the concurrent generation of two characteristic waves dealing with dual modes and introduces three physical parameters: nonlinearity, phase velocity, and dispersive factor. In the context of photonics, NLSE models the propagation of soliton pulses over intercontinental distances. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. We analyze the multi‐waves method, homoclinic breather approach, and interactional solution with the double ‐functions procedure, and their applications for this equation are obtained using logarithmic transformation. The multi‐wave method is a well‐known phenomenon in nonlinear science that describes the interaction of three waves that satisfy certain resonance conditions. A breather wave is a localized and oscillatory solution that maintains its shape over time. Finally, we will discuss the dynamics of our newly obtained solutions with the help of graphs by assigning appropriate values to the parameters. The proposed methods are straight and aggressive, so the approved form can be extended for more nonlinear models. The findings are exceptional in comparison to previous findings in the literature. These outcomes may have significance for additional investigation of such frameworks to handle the nonlinear issues in applied sciences. The obtained results help us understand fluid propagation and incompressible fluids.

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Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

Cited by 7 publications

References 55 publications

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

A family of iterative methods to solve nonlinear problems with applications in fractional differential equations

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

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