Integrable Kuralay Equations: Geometry, Solutions and Generalizations

Sagidullayeva, Zhanna; Nugmanova, Gulgassyl; Myrzakulov, Ratbay; Serikbayev, Nurzhan

doi:10.3390/sym14071374

Cited by 42 publications

(4 citation statements)

References 39 publications

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“…Through this investigation, we aim to analyze the notable characteristics associated with these soliton solutions by adjusting the system parameters. Exploring solitary wave solutions for nonlinear equations is pivotal in unraveling various nonlinear physical phenomena [28][29][30][31][32][33][34][35]. Nonlinear wave phenomena manifest across a spectrum of engineering and scientific domains, encompassing fluid dynamics, plasma physics, optics, biology, condensed matter physics, and beyond [1,9].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Muniyappan,

Manikandan,

Saparbekova

et al. 2024

Symmetry

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This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, we derive an abundant soliton solution for the transformed system. By plugging these explicit solutions back into the wave transformation, we obtain dark and singular soliton solutions for the Hirota equation. The dynamic evolution of dark soliton profiles is then demonstrated, with a focus on varying physically significant parameters such as wave frequency, strength of third-order dispersion, and wave number. Furthermore, a comprehensive analysis is examined to elucidate how the dark and singular soliton profiles undergo deformation in the background influenced by these arbitrary parameters. The findings presented in this study offer valuable insights that could potentially guide experimental manipulation of dark solitons in optical fibers.

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Section: Introductionmentioning

confidence: 99%

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Muniyappan,

Manikandan,

Saparbekova

et al. 2024

Symmetry

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“…Different kind of study of this model have been done in the literature. Instantly, simplest soliton solutions of this model have been gained by utilizing the Hirota bilinear scheme [10]. The fundamental purpose of the work is to explore new analytical wave solutions to the space-time fractional Kuralay-II equations (K-IIAE and K-IIBE) with truncated Mfractional derivative based on exp a function, extended sinh-Gordon equation expansion and generalized Kudryashov schemes.…”

Section: Introductionmentioning

confidence: 99%

New analytical wave solutions to the M-fractional Kuralay-II equations based on three distinct schemes

Raheel

Zafar

Ali

et al. 2023

Preprint

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This article is about, the new analytical wave solutions of Kuralay-II equations (K-IIAE and K-IIBE) along new definition of derivative have been explored. For this purpose, expa function, extended sinh-Gordon equation expansion scheme and generalized Kudryashov schemes have been utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by Mathematica tool. Our gained solutions are newer than the present solutions in the literature. The gained results can also be fruitful for the development of model in future. The schemes used in this research are effective, easy and reliable to handle the other fractional non-linear partial differential equations (FNLPDEs).

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“…Different kinds of study of this model are reported in the literature. The simplest soliton solutions of this model were obtained by utilizing the Hirota bilinear scheme [29]. Analytical solitary wave solutions were obtained by applying the new auxiliary equation method [30].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

Zafar,

Raheel,

Ali

et al. 2023

Symmetry

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This article concerns new analytical wave solutions of the Kuralay-II equations (K-IIAE and K-IIBE) with exploration of a new definition of the derivative. This model is used in various fields, like nonlinear optics, ferromagnetic materials and optical fibers. For this purpose, the expa function, the extended sinh-Gordon equation expansion scheme, and the generalized Kudryashov schemes were utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by the Mathematica tool. Some of the solutions are explained with 2-D, 3-D and contour plots using the Mathematica tool. The solutions obtained succede the present solutions in the literature. For the first time, the effect of the fractional derivative on the solutions is also shown graphically for this model. The analytical wave solutions are highly desirable as they offer insights into the underlying physics or mathematics of a system and provide a framework for further analysis. The results obtained can also be fruitful for the development of models in the future. The schemes used in this research are effective, easy to apply, and reliably handle other fractional non-linear partial differential equations.

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Integrable Kuralay Equations: Geometry, Solutions and Generalizations

Cited by 42 publications

References 39 publications

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

New analytical wave solutions to the M-fractional Kuralay-II equations based on three distinct schemes

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

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