Wave interactions and structures of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Jisha, C. R.; Dubey, Ritesh Kumar

doi:10.1007/s11071-022-07816-6

“…2, the arrows may gather together or We can observe that at three points at zero near the real part of τ arrows in the stream plot form spirals around particular points, indicating the presence of a spiral singularity. This suggests that the complex function has a branch cut or a spiral pattern of behavior 2 Singularities, on the other hand, are points where a complex function is not defined or behaves in an unusual manner. (…”

Section: Solution Based On Polynomial Functionmentioning

confidence: 99%

“…The transformed equation, which we refrain from proving due to its inherent complexity, can be solved effectively using the unified method. Such solutions are significant as they find practical utility in investigating wave in- teractions, as noted in [2]. In general, the solution to equation (1) can be expressed as follows:…”

Section: Solution Of the Form -Log(u) Xmentioning

confidence: 99%

“…The nonlinear partial differential equation (PDE) arises in various areas, including nonlinear optics, chemical kinetics, geochemistry, optical fibers, solid-state physics, plasma physics, fluid mechanics, and fluid dynamics [1][2][3][4]. The importance of analytical solutions of the nonlinear PDEs lies in their ability to provide a deeper understanding of the underlying physics, offer insight into the behavior of complex systems, and serve as valuable tools for validating numerical methods [5].…”

Section: Introductionmentioning

confidence: 99%

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Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

Jisha,

Jang

2024

Nonlinear Dyn

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This study comprehensively explores a unified methodology for deriving exact solutions to the fractional modified (3+1) dimensional Kudryashov-Sinelshchikov (KS) equation featuring variable coefficients. The fractional KS equation, which incorporates fractional local M-derivatives, presents a significant challenge because of its inherent nonlinearity and the introduction of spatially varying coefficients. Of paramount importance are these variable coefficients, as they introduce spatial dependence and intricately capture spatial variations within the equation. This complexity in spatial variation poses a formidable challenge in obtaining exact solutions. Our analytical examination offers profound insights into the intricate interplay between diverse variable coefficients and fractional parameters. This comprehensive analysis greatly enhances our capacity to interpret solutions across various scenarios, enriching our understanding of the nuanced behavior exhibited by the fractional Kudryashov-Sinelshchikov equation. Our investigation encompasses a diverse range of solution forms, including fractional, polynomial, exponential, and others. The outcomes of

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“…The nonlinear partial differential equation (PDE) arises in various areas, including nonlinear optics, chemical kinetics, geochemistry, optical fibers, solid-state physics, plasma physics, fluid mechanics, and fluid dynamics [1][2][3][4]. The importance of analytical solutions of the nonlinear PDEs lies in their ability to provide a deeper understanding of the underlying physics, offer insight into the behavior of complex systems, and serve as valuable tools for validating numerical methods [5].…”

Section: Introductionmentioning

confidence: 99%

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

CR,

Jang

2023

Preprint

0

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This study comprehensively explores a unified methodology for deriving exact solutions to the fractional modified (3+1) dimensional Kudryashov-Sinelshchikov (KS) equation featuring variable coefficients. The fractional KS equation, which incorporates fractional local M-derivatives, presents a significant challenge because of its inherent nonlinearity and the introduction of spatially varying coefficients. Of paramount importance are these variable coefficients, as they introduce spatial dependence and intricately capture spatial variations within the equation. This complexity in spatial variation poses a formidable challenge in obtaining exact solutions. Our analytical examination offers profound insights into the intricate interplay between diverse variable coefficients and fractional parameters. This comprehensive analysis greatly enhances our capacity to interpret solutions across various scenarios, enriching our understanding of the nuanced behavior exhibited by the fractional Kudryashov-Sinelshchikov equation. Our investigation encompasses a diverse range of solution forms, including fractional, polynomial, exponential, and others. The outcomes of this study hold profound implications for an extensive array of scientific domains, spanning mathematical physics, fluid dynamics, and nonlinear optics. Furthermore, this research employs advanced data visualization techniques, comprising 3D plots, contour plots, and stream plots, to facilitate a deep comprehension of intricate physical phenomena. These visual aids concurrently illustrate how analytical solutions are influenced by varying conditions. Ams classification 2010: 45K05, 45G10, 83C15, 35Q35, 35Q68 , 35Q80

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Stability analysis and dispersive optical solitons of fractional Schrödinger–Hirota equation

Akram

¹

,

Ahmad

²

,

Rehman

³

et al. 2023

Opt Quant Electron

21

0

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Wave interactions and structures of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Cited by 11 publications

References 56 publications

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

Stability analysis and dispersive optical solitons of fractional Schrödinger–Hirota equation

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