Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Xu, Bo; Zhang, Yufeng; Zhang, Sheng

doi:10.1155/2021/6669087

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…We investigate the evolution of the perturbation ΞðX; TÞ using the concept of linear stability analysis. Substituting Equation (48) into Equation ( 4) and linearizing the result in ΞðX; TÞ, we acquire…”

Section: Modulation Instability Analysis Of the Nonlinear Gpementioning

confidence: 99%

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The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

Gao,

Baskonus

2023

Advances in Mathematical Physics

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In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail.

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Section: Modulation Instability Analysis Of the Nonlinear Gpementioning

confidence: 99%

“…In [46], bipolar cubic fuzzy graphs have been studied. The shallow ocean-waves and rogue waves with translational coordination have been observed in [47,48]. The influence of Woods-Saxon potential was presented in [49].…”

Section: Introductionmentioning

confidence: 98%

The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

Gao,

Baskonus

2023

Advances in Mathematical Physics

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Extraction of Optical Solitons for Conformable Perturbed Gerdjikov–Ivanov Equation via Two Integrating Techniques

Vivas-Cortez,

Sadaf,

Arshed

et al. 2024

Advances in Mathematical Physics

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The perturbed Gerdjikov–Ivanov equation has immersed applications and significance in photonic crystal fibers and fiber optics. Extracting soliton solutions of the proposed equation has always been a challenging task for researchers. In this article, soliton solutions of governing equation are formed by using two very good and reliable analytical techniques, two variables (G′/G, 1/G) expansion method and generalized projective Riccati equation method. These methods are well‐known and widely employed. The constraint conditions for newly constructed solutions are also specified. Furthermore, the obtained solutions can be utilized in nonlinear physical situations. Surface plots of the solution functions are also given in this paper to highlight the physical significance. Fractional effects are also discussed through various line graphs.

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Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation

Shi

Zhang

2023

THERM SCI

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In this paper, a local fractional generalized Broer-Kaup (gBK) system is first de?rived from the linear matrix problem equipped with local space and time fractional partial derivatives, i.e, fractional Lax pair. Based on the derived fractional Lax pair, the second kind of fractional Darboux transformation (DT) mapping the old potentials of the local fractional gBK system into new ones is then established. Finally, non-differentiable frcational odd-soliton solutions of the local fractional gBK system are obtained by using two basic solutions of the derived fractional Lax pair and the established fractional DT. This paper shows that the DT can be extended to construct non-differentiable fractional soliton solutions of some local fractional non-linear evolution equations in mathematical physics.

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Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Cited by 3 publications

References 37 publications

The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

Extraction of Optical Solitons for Conformable Perturbed Gerdjikov–Ivanov Equation via Two Integrating Techniques

Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation

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