Bifurcation analysis and new waveforms to the first fractional WBBM equation

Scientific Reports, Journal Year: 2024, Volume and Issue: 14(1)

Published: May 24, 2024

Abstract This research focuses on bifurcation analysis and new waveforms for the first fractional 3D Wazwaz–Benjamin–Bona–Mahony (WBBM) structure, which arises in shallow water waves. The linear stability technique is also employed to assess of mentioned model. suggested equation’s dynamical system obtained by applying Galilean transformation achieve our goal. Subsequently, bifurcation, chaos, sensitivity model are conducted principles planar system. We obtain periodic, quasi-periodic, chaotic behaviors Furthermore, we introduce delve into diverse solitary wave solutions, encompassing bright soliton, dark kink wave, periodic waves, anti-kink These solutions visually presented through simulations, highlighting their distinct characteristics existence. results highlight effectiveness, brevity, efficiency integration methods. They suggest applicability delving more intricate nonlinear models emerging modern science engineering scenarios. novelty this lies its detailed governing model, provides insights complex dynamics varied structures. study advances understanding properties combining analysis, behavior, waveform characteristics, assessments.

Language: Английский

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Qualitative behavior and variant soliton profiles of the generalized P-type equation with its sensitivity visualization

Alexandria Engineering Journal, Journal Year: 2024, Volume and Issue: 104, P. 292 - 305

Published: June 28, 2024

Language: Английский

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Optical soliton stability in zig-zag optical lattices: comparative analysis through two analytical techniques and phase portraits

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: 112(24), P. 22221 - 22243

Published: Aug. 21, 2024

Abstract This article explores the examination of widely employed zig-zag optical lattice model for cold bosonic atoms, which is commonly utilized to depict nonlinear wave in fluid mechanics and plasma physics. The focus on obtaining soliton solutions optics investigating their physical properties. A transformation initially applied convert a partial differential equation (PDE) into an ordinary (ODE). Soliton are subsequently obtained through application two distinct methods, namely generalized logistic method Sardar sub-equation method. These include bright, dark, combined dark-bright, chirped type solitons, bell-shaped, periodic, W-shape, kink solitons. In this paper, derived from analytical approaches were compared enhance understanding behavior discussed model. have significant implications across various fields such as physics, dynamics, optics, communication technology. Furthermore, 3D 2D graphs generated phenomena by assigning appropriate constant parameters. qualitative evaluation undisturbed planar system involves analysis phase portraits within bifurcation theory. Subsequently, introduction outward force carried out induce disruption, chaotic unveiled. detection trajectory perturbed achieved plots, time scale Lyapunov exponents. stability examined addressed under initial conditions. Finally, sensitivity assessment consideration using Runge–Kutta results study innovative not been previously investigated consideration. underscore reliability, simplicity, effectiveness these techniques analyzing variety models found mathematical physics engineering disciplines.

Language: Английский

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Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method

Results in Physics, Journal Year: 2024, Volume and Issue: 64, P. 107882 - 107882

Published: July 26, 2024

This document elaborates on a newly introduced analytical method known as the "Variable Coefficient Generalized Abel Equation Method," proposed by Hashemi in (2024), designed specifically for addressing two-mode Cahn–Allen equation. Diverging from conventional techniques that heavily rely constant coefficient ordinary differential equations and auxiliary equations, our innovatively incorporates variable within sub-equation framework. Demonstrating its versatility, we apply this innovative technique to equation, showcasing effectiveness efficiency through derivation of solutions. Notably, emerges promising tool tackling complex nonlinear partial prevalent fluid dynamics wave propagation scenarios. Beyond merely expanding repertoire available tools, approach contributes advancing solutions various models realm mathematical physics. Various forms exact solutions, including exponential-type Kink solitons, dark bright soliton are obtained model under consideration. Moreover, delve into analysis bifurcation, chaotic behavior, sensitivity context model, further enhancing depth breadth study. Three equilibria analyzed across classifications, center point, focus saddle node point. Chaotic behavior corresponding dynamical system is considered adding function ω1sin(ω2ζ). Lastly, conducted examining different parameters imposing noise initial conditions.

Language: Английский

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Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

Qualitative Theory of Dynamical Systems, Journal Year: 2024, Volume and Issue: 23(S1)

Published: Oct. 3, 2024

Language: Английский

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Multiple interaction solutions, parameter analysis, chaotic phenomena and modulation instability for a (3+1)-dimensional Kudryashov–Sinelshchikov equation in ideal liquid with gas bubbles

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: Sept. 2, 2024

Language: Английский

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Chaotic response, multistability and new wave structures for the generalized coupled Whitham–Broer–Kaup–Boussinesq–Kupershmidt system with a novel methodology

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 190, P. 115755 - 115755

Published: Nov. 21, 2024

Language: Английский

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Dynamical analysis, chaos and multistability of the resonant third-order nonlinear Schrödinger equation through phase portraits

Modern Physics Letters A, Journal Year: 2025, Volume and Issue: unknown

Published: March 28, 2025

The main aim of this paper is to navigate qualitative research deal with chaotic behavior, bifurcation, and sensitivity analysis through phase diagrams. model under consideration a resonant third-order nonlinear Schrödinger equation describing wave propagation in fiber optics. converted into ordinary differential equations using traveling hypothesis, which utilizes the Galilean transformation turn planar dynamical system. Further, dynamics time-dependent system are investigated chaos theory. portraits, time series, Poincaré maps Lyapunov exponent used identify behavior self-governing systems. Four distinct initial conditions examine model’s sensitivity. Additionally, soliton solutions examined include bright envelope solutions, dark periodic their existence criterion.

Language: Английский

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Lump solitions, fractal soliton solutions, superposed periodic wave solutions and bright-dark soliton solutions of the generalized (3+1)-dimensional KP equation via BNNM

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: 112(19), P. 17345 - 17361

Published: July 8, 2024

Language: Английский

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A fuzzy semi-analytical approach for modeling uncertainties in solitary wave solution of coupled nonlinear Boussinesq equations

Physica Scripta, Journal Year: 2024, Volume and Issue: 99(10), P. 105218 - 105218

Published: Aug. 22, 2024

Abstract This article presents the precise solitary wave solution (SWS) of nonlinear coupled Boussinesq equations (BEs) in shallow water using Homotopy Perturbation Transform Method (HPTM) and Fuzzy HPTM (FHPTM). The study introduces a fuzzy model for BEs by incorporating uncertainties depth coefficients. effectiveness FHPTM is demonstrated through comparison with exact crisp case, double parametric approach to highlight fuzziness solution. Numerical results under various scenarios are examined understand behavior SWS. compared those derived from Adomian Decomposition (ADM). show good agreement both numerical techniques.

Language: Английский

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