Dynamics of quasi-periodic, bifurcation, sensitivity and three-wave solutions for

This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a numb...

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Bibliographic Details
Published in:PloS one Vol. 19; no. 8; p. e0305094
Main Authors: Rafiq, Muhammad Hamza, Riaz, Muhammad Bilal, Basendwah, Ghada Ali, Raza, Nauman, Rafiq, Muhammad Naveed
Format: Journal Article
Language:English
Published: Public Library of Science 27.08.2024
Subjects:
Analysis
Bifurcation theory
Differential equations
Health aspects
Symmetry (Biology)
Pakistan
ISSN:1932-6203, 1932-6203
Online Access:Get full text
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Summary:This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0305094