Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

Alqahtani, Rubayyi T.; Kaplan, Melike

doi:10.3390/math12050720

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Differential equations have a strong physical background and have important applications in fields such as natural science and technical science. The solutions and properties of differential equations are significant [1,2]. For example, the stability of a differential equation not only reflects the characteristics of the equation itself, it plays a role in practical model analysis [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

Chen,

Wei,

Song

et al. 2024

Mathematics

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In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelty lies. The Painlevé integrability is tested by the method of Weiss, Tabor, and Carnevale (WTC) with the simplified form of Krustal. The rational solutions are derived by the Hirota bilinear method, where the formulae of the solutions are represented in terms of determinants. Furthermore the fundamental rogue wave solutions are obtained under certain parameter restrains in rational solutions. Finally the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. These rogue wave solutions have comprehensive implications for two-dimensional surface water waves in the ocean.

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Section: Introductionmentioning

confidence: 99%

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

Chen,

Wei,

Song

et al. 2024

Mathematics

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A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques

Hossain,

Rasid,

Abouelfarag

et al. 2024

Open Physics

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Soliton solutions play a crucial role in modeling stable phenomena across optical communications, fluid dynamics, and plasma physics, owing to their stability and persistence in solving nonlinear equations. This study centers on the extended Sakovich equation, emphasizing the importance of soliton solutions in predicting and controlling localized wave behaviors, which advances nonlinear dynamics and its various applications due to its integrable properties and flexible soliton characteristics. This equation is applicable across diverse fields such as fluid dynamics, nonlinear optics, and plasma physics, where it effectively models nonlinear wave phenomena, including solitons and shock waves. Additionally, it provides crucial insights into wave propagation in biological systems and acoustics, making it a valuable tool for analyzing complex wave dynamics. Additionally, we investigate bifurcation and modulation instability within this equation, employing the improved Sardar subequation method and the ℛ ′ ℛ , 1 ℛ \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{{ {\mathcal R} }^{^{\prime} }}{ {\mathcal R} },\frac{1}{ {\mathcal R} }\right) method to derive solitary wave solutions. These methods yield a diverse range of waveforms – hyperbolic, trigonometric, and rational functions – validated rigorously using Mathematica software for accuracy. Graphical representations vividly display various soliton patterns, such as singular, multi-singular, periodic singular, kink, anti-kink, bell-shaped, Kuznetsov–Ma Breather, and parabolic-shaped, highlighting their effectiveness in revealing innovative solutions. Furthermore, a comparative analysis verified the novelty of our derived soliton solutions. This research significantly contributes to advancing soliton solutions for the Sakovich equation, promising diverse applications across scientific disciplines.

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Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

Cited by 2 publications

References 31 publications

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques

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