Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis

Maria Luz Gandarias, Nauman Raza (), Muhammad Umair and Yahya Almalki
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Maria Luz Gandarias: Department of Mathematics, University of Cadiz, 11510 Puerto Real, Spain
Nauman Raza: Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan
Muhammad Umair: Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
Yahya Almalki: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Mathematics, 2024, vol. 13, issue 1, 1-18

Abstract: This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(- S ( χ )) expansion technique has been utilized to uncover closed-form solitary wave solutions. The findings reveal a range of soliton types, including exponential, rational, hyperbolic, and trigonometric functions, represented as bright, singular, rational, periodic, and new solitary waves. These results are illustrated numerically and accompanied by insightful physical interpretations, enriching the comprehension of the complex dynamics modeled by these equations. Our approach’s novelty lies in applying a new methodology to this problem, yielding a variety of novel optical soliton solutions. Additionally, we employ bifurcation and chaos techniques for a qualitative analysis of the model, extracting a planar system from the original equation and mapping all possible phase portraits. A thorough sensitivity analysis of the governing equation is also presented. These results highlight the effectiveness of our methodology in tackling nonlinear problems in both mathematics and engineering, surpassing previous research efforts.

Keywords: (4+1)-D KdV–CBS equation; generalized exp(-?(?)) expansion method; novel solitons; dynamic study of bifurcation and chaotic behavior; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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