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Soliton solutions with bifurcation, sensitivity, chaotic and stability analysis of the (2+1)-dimensional Zoomeron
Arooma Zainab1, Khaled M Saad2, Muhammad Abbas3
1Department of Mathematics, University of Sargodha, 40100, Sargodha, Pakistan.
Scientific Reports
|December 12, 2025
Summary
This study explores the (2+1)-dimensional Zoomeron equation, revealing novel V-pattern and W-shaped soliton solutions. The research details their complex dynamics and stability using advanced analytical and graphical methods.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Soliton Theory
Background:
- The (2+1)-dimensional Zoomeron equation models complex nonlinear wave phenomena.
- Understanding diverse soliton solutions is crucial for nonlinear system analysis.
Purpose of the Study:
- To investigate the dynamical behavior of the (2+1)-dimensional Zoomeron equation.
- To derive and analyze novel soliton solutions, including V-pattern and W-shaped solitons.
- To explore the transition from periodic to chaotic behavior in these nonlinear waves.
Main Methods:
- Application of the generalized Riccati equation mapping method.
- Utilizing traveling wave transformations to reduce the partial differential equation to an ordinary differential equation.
- Employing bifurcation, chaotic, sensitivity, and stability analyses.
Main Results:
- Identification of various soliton solutions: kink, anti-kink, bright, dark, periodic, singular, V-pattern, and W-shaped solitons.
- First-time presentation of V-pattern and W-shaped solitons for the Zoomeron equation.
- Demonstration of transitions from periodic to chaotic dynamics and verification of soliton stability via modulation instability analysis.
Conclusions:
- The generalized Riccati equation mapping method effectively reveals complex soliton solutions and dynamics.
- The study provides new insights into the nonlinear wave phenomena of the Zoomeron model.
- Graphical representations highlight the intricate behaviors and properties of the derived soliton solutions.
Keywords:
(2+1)-Dimensional Zoomeron equationDynamical studyGeneralized Riccati equation mapping methodSoliton solutionsStabilityMore Related Videos
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