Bifurcation and chaos analysis of the Kadomtsev Petviashvili-modified equal width equation using a novel analytical method: describing ocean waves

Amna Mumtaz; Muhammad Shakeel; Abdul Manan; Marouan Kouki; Nehad Ali Shah; Amna Mumtaz; Muhammad Shakeel; Abdul Manan; Marouan Kouki; Nehad Ali Shah

doi:10.3934/math.2025439

AIMS Mathematics

2025, Volume 10, Issue 4: 9516-9538. doi: 10.3934/math.2025439

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Bifurcation and chaos analysis of the Kadomtsev Petviashvili-modified equal width equation using a novel analytical method: describing ocean waves

1.
Department of Mathematics, Faculty of Basic Sciences, University of Wah, Wah Cantt 47040, Pakistan; amna.mumtazsyed@gmail.com, muhammad.shakeel@uow.edu.pk
2.
Department of Mathematics, Faculty of Sciences, Superior University, Main Campus Lahore, Pakistan; abdul.manan@superior.edu.pk
3.
Department of Information System, Faculty of Computing and Information Technology, Northern Border University, Rafha, Saudi Arabia
4.
Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
^† These authors contributed equally to this work and are co-first authors

Received: 13 February 2025 Revised: 08 April 2025 Accepted: 15 April 2025 Published: 25 April 2025
MSC : 34G20, 35A20, 35C07, 35C08

This work investigated the Kadomtsev Petviashvili-modified equal width (KP-mEW) equation describing ocean waves. Our focus was on the analysis of the KP-mEW equation from various angles, including the study of soliton solutions, bifurcation analysis, multistability, and Lyapunov exponents. First, a transformation was used to transform the partial differential equation (PDE) into an ordinary differential equation (ODE), from which the soliton solutions were obtained by using a new modified (G'/G²)-expansion method. We investigated different types of solutions of the KP-mEW equation with various parameters, including kink, periodic, singular periodic, singular kink, and singular periodic-kink solutions. We also simulated 3D and 2D plots for some solutions to enhance the visualizations. These graphical representations provide important information about the patterns and dynamics of the solutions, leading to a strong understanding of the behavior and applicability of the model. We also observed the chaotic behavior of the system by adding a perturbation term and analyzed the chaotic behavior through bifurcation plots, multistability and time series analysis, and Lyapunov exponents and obtained various dynamic modes such as periodic and quasi-periodic types. A comparison of the obtained solutions with the existing solutions was also presented in the form of Table 1.
- new modified (G'/G²)-expansion method,
- nonlinear KP-mEW equation,
- traveling wave solution,
- exact solutions,
- soliton solutions,
- chaotic analysis
Citation: Amna Mumtaz, Muhammad Shakeel, Abdul Manan, Marouan Kouki, Nehad Ali Shah. Bifurcation and chaos analysis of the Kadomtsev Petviashvili-modified equal width equation using a novel analytical method: describing ocean waves[J]. AIMS Mathematics, 2025, 10(4): 9516-9538. doi: 10.3934/math.2025439

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Abstract

This work investigated the Kadomtsev Petviashvili-modified equal width (KP-mEW) equation describing ocean waves. Our focus was on the analysis of the KP-mEW equation from various angles, including the study of soliton solutions, bifurcation analysis, multistability, and Lyapunov exponents. First, a transformation was used to transform the partial differential equation (PDE) into an ordinary differential equation (ODE), from which the soliton solutions were obtained by using a new modified (G'/G²)-expansion method. We investigated different types of solutions of the KP-mEW equation with various parameters, including kink, periodic, singular periodic, singular kink, and singular periodic-kink solutions. We also simulated 3D and 2D plots for some solutions to enhance the visualizations. These graphical representations provide important information about the patterns and dynamics of the solutions, leading to a strong understanding of the behavior and applicability of the model. We also observed the chaotic behavior of the system by adding a perturbation term and analyzed the chaotic behavior through bifurcation plots, multistability and time series analysis, and Lyapunov exponents and obtained various dynamic modes such as periodic and quasi-periodic types. A comparison of the obtained solutions with the existing solutions was also presented in the form of Table 1.

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