Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model

Abstract This research explores the (2+1)-D nonlinear electrical transmission line equation (NLETLE), highlighting its unique localized wave solutions and the interactions that arise from them. Through the application of a novel multivariate generalized exponential differential function technique an...

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Main Authors: Muhammad Abdaal Bin Iqbal, Muhammad Zubair Raza, Maasoomah Sadaf, Ghazala Akram, Muhammad Yousaf, Homan Emadifar, Wael W. Mohammed, Karim K. Ahmed
Format: Article
Language:English
Published: Nature Portfolio 2025-07-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-08795-5
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author Muhammad Abdaal Bin Iqbal
Muhammad Zubair Raza
Maasoomah Sadaf
Ghazala Akram
Muhammad Yousaf
Homan Emadifar
Wael W. Mohammed
Karim K. Ahmed
author_facet Muhammad Abdaal Bin Iqbal
Muhammad Zubair Raza
Maasoomah Sadaf
Ghazala Akram
Muhammad Yousaf
Homan Emadifar
Wael W. Mohammed
Karim K. Ahmed
author_sort Muhammad Abdaal Bin Iqbal
collection DOAJ
description Abstract This research explores the (2+1)-D nonlinear electrical transmission line equation (NLETLE), highlighting its unique localized wave solutions and the interactions that arise from them. Through the application of a novel multivariate generalized exponential differential function technique and generalized logistic equation approach, we have successfully generated a diverse array of new structures, particularly characterized by bright soliton, bright-singular soliton, kink soliton, and periodic waveforms. These solutions play a crucial role in demonstrating the complex structure and varied dynamics that are characteristic of nonlinear systems in higher dimensions. To achieve a comprehensive understanding, we depict these solutions using 3D surface density plots and line graphs. Additionally, we analyze the dynamic behavior of the system through bifurcation analysis, which is graphically represented by phase portraits. Subsequently, we incorporate periodic functions into the dynamical system to investigate the nonlinear properties of the dynamical system, in order to uncover its chaotic behavior, utilizing concepts derived from the theory of chaos. The observation and confirmation of chaotic behavior are achieved by employing a range of chaos detection tools. In addition, we conduct a sensitivity analysis to determine how minor modifications in the system affect its overall behavior, which in turn provides greater insight into its robustness and ability to respond to perturbations. By varying the initial conditions, we analyze multistability, which highlights the system’s ability to display multiple stable states influenced by choosing suitable parametric values. The results acquired from this research are new and significant for the continued exploration of the (2+1)-D NLETLE, offering direction for future scholars.
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spelling doaj-art-1915b040e10f46f0baa20ffcf6ba5a9a2025-08-20T03:03:40ZengNature PortfolioScientific Reports2045-23222025-07-0115112210.1038/s41598-025-08795-5Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line modelMuhammad Abdaal Bin Iqbal0Muhammad Zubair Raza1Maasoomah Sadaf2Ghazala Akram3Muhammad Yousaf4Homan Emadifar5Wael W. Mohammed6Karim K. Ahmed7Department of Mathematics, University of the PunjabDepartment of Mathematics, University of the PunjabDepartment of Mathematics, University of the PunjabDepartment of Mathematics, University of the PunjabDepartment of Mathematics, Government College University FaisalabadDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical SciencesDepartment of Mathematics, College of Science, University of Ha’ilDepartment of Mathematics, Faculty of Engineering, German International University (GIU)Abstract This research explores the (2+1)-D nonlinear electrical transmission line equation (NLETLE), highlighting its unique localized wave solutions and the interactions that arise from them. Through the application of a novel multivariate generalized exponential differential function technique and generalized logistic equation approach, we have successfully generated a diverse array of new structures, particularly characterized by bright soliton, bright-singular soliton, kink soliton, and periodic waveforms. These solutions play a crucial role in demonstrating the complex structure and varied dynamics that are characteristic of nonlinear systems in higher dimensions. To achieve a comprehensive understanding, we depict these solutions using 3D surface density plots and line graphs. Additionally, we analyze the dynamic behavior of the system through bifurcation analysis, which is graphically represented by phase portraits. Subsequently, we incorporate periodic functions into the dynamical system to investigate the nonlinear properties of the dynamical system, in order to uncover its chaotic behavior, utilizing concepts derived from the theory of chaos. The observation and confirmation of chaotic behavior are achieved by employing a range of chaos detection tools. In addition, we conduct a sensitivity analysis to determine how minor modifications in the system affect its overall behavior, which in turn provides greater insight into its robustness and ability to respond to perturbations. By varying the initial conditions, we analyze multistability, which highlights the system’s ability to display multiple stable states influenced by choosing suitable parametric values. The results acquired from this research are new and significant for the continued exploration of the (2+1)-D NLETLE, offering direction for future scholars.https://doi.org/10.1038/s41598-025-08795-5(2+1)-D NLETLEInnovative analytical techniquesBifurcation analysisChaotic behaviorSensitivity analysisMultistability analysis
spellingShingle Muhammad Abdaal Bin Iqbal
Muhammad Zubair Raza
Maasoomah Sadaf
Ghazala Akram
Muhammad Yousaf
Homan Emadifar
Wael W. Mohammed
Karim K. Ahmed
Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
Scientific Reports
(2+1)-D NLETLE
Innovative analytical techniques
Bifurcation analysis
Chaotic behavior
Sensitivity analysis
Multistability analysis
title Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
title_full Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
title_fullStr Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
title_full_unstemmed Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
title_short Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model
title_sort solitary waves bifurcation chaos sensitivity and multistability of electrical transmission line model
topic (2+1)-D NLETLE
Innovative analytical techniques
Bifurcation analysis
Chaotic behavior
Sensitivity analysis
Multistability analysis
url https://doi.org/10.1038/s41598-025-08795-5
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