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Chaotic behavior, sensitivity analysis and Jacobian elliptic function solution of M-fractional paraxial wave with
Md Mamunur Roshid1,2, Mohammad Safi Ullah3, M M Rahman1
1Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladeshig.
Plos One
|February 21, 2025
Summary
This study explores the M-fractional paraxial wave equation with Kerr nonlinearity, generating diverse optical wave structures using the extended Jacobian elliptic function expansion (EJEFE) method and analyzing chaotic phenomena.
Area of Science:
- Nonlinear Optics
- Mathematical Physics
- Wave Propagation
Background:
- The paraxial wave equation is crucial for modeling wave propagation, particularly beam-like structures like laser beams and optical solitons.
- It balances linear dispersion and nonlinear effects, essential for understanding diffraction, focusing, and self-phase modulation in optical fibers.
- This equation is vital for comprehending optical soliton characteristics and dynamics in various optical systems.
Purpose of the Study:
- To investigate the paraxial approximation of the M-fractional paraxial wave equation with Kerr law nonlinearity.
- To generate a variety of wave structures and analyze chaotic phenomena within the model.
- To demonstrate the adaptability and usefulness of the extended Jacobian elliptic function expansion (EJEFE) method.
Main Methods:
- Application of the extended Jacobian elliptic function expansion (EJEFE) method.
- Qualitative analysis of chaotic phenomena through phase portraits for various parameter values.
- Sensitivity analysis for perturbed coefficients and investigation of chaotic/quasi-periodic phenomena using time series and phase patterns.
Main Results:
- Generation of diverse wave structures including periodic waves, lump-periodic waves, breather waves, kink-bell waves, and double-periodic waves.
- Detailed analysis of phase portraits revealing system behavior and insights into chaotic dynamics.
- Identification of chaotic and quasi-periodic phenomena under external periodic forcing.
Conclusions:
- The EJEFE method is effective for generating complex optical solutions for the M-fractional paraxial wave equation.
- The study provides insights into the dynamics and chaotic behavior of the investigated wave equation.
- The findings have implications for understanding wave dynamics in optical systems and optical fibers.
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