Nonautonomous lump waves of a (3+1)-dimensional Kudryashov–Sinelshchikov equation with variable coefficients in bubbly liquids

Hu, Zhengran; Wang, Feifan; Zhao, Yue; Lan, Zhong-Zhou; Li, Min

doi:10.1007/s11071-021-06570-5

Cited by 9 publications

(2 citation statements)

References 58 publications

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“…Their research likely explores the analytical properties, solution techniques, and implications of the KS equation, contributing to understanding nonlinear wave phenomena in fluid dynamics. The (3+1)-dimensional variable coefficient Kudryashov and Sinelshchikov (vcKS) equation with regular time derivative model solved using Hirota's bilinear and other methods are discussed in [20][21][22][23][24][25]. In the context of plasmas, the KS equation provides a mathematical framework to investigate the dynamics of ion-acoustic solitons.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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“…The nonautonomous lump solutions of the (3+1)-dimensional variable-coefficient Kudryashov and Sinelshchikov (vcKS) equation using Hirota's bilinear technique is discussed in [29]. The 3D vcKS equation is solved by the Jacobi elliptic function method is discussed in [30].…”

Section: Introductionmentioning

confidence: 99%

The exact solutions for Kudryashov and Sinelshchikov equation with variable coefficients

Jisha¹,

Dubey²,

Benton³

et al. 2022

Phys. Scr.

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The Kudryashov and Sinelshchikov (KS) equation address pressure waves in liquid-gas bubble mixtures while considering heat transport and viscosity. This study mainly includes two types of generalized solutions: polynomial function traveling wave solutions and rational function traveling wave solutions. In this study, we constructed the KS equation's exact traveling and solitary wave solutions with variable coefficients by the generalized unified method (GUM). These newly created solutions play a significant role in mathematical physics, optical fiber physics, plasma physics, and other applied sciences disciplines. We illustrated the dynamical behavior of the discovered solutions in three dimensions. We proposed the possibility of discussing wave interaction and other wave structures using bilinear form related to the Hirota method for the fractional solution.

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Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota’s bilinear method

Alquran

Alhami

2022

Nonlinear Dyn

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Nonautonomous lump waves of a (3+1)-dimensional Kudryashov–Sinelshchikov equation with variable coefficients in bubbly liquids

Cited by 9 publications

References 58 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

The exact solutions for Kudryashov and Sinelshchikov equation with variable coefficients

Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota’s bilinear method

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