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Summary

This study explores the Akbota equation, crucial for nonlinear dynamics in optics and magnetism. Researchers derived exact solutions, revealing kink, bright, and dark solitons for optical fiber applications.

Keywords:
Akbota equationExact solutionsKumar–Malik methodNew Kudryashov methodRiccati equation method

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Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Optics and magnetism

Background:

  • The Akbota equation (AE) models integrable systems with solitary waves, fundamental in nonlinear dynamics.
  • AE is vital for understanding optical solitons in nonlinear optical fibers, essential for robust fiber-optic communication.
  • Investigating AE's dynamics aids in comprehending wave propagation and stability in various scientific fields.

Purpose of the Study:

  • To explore the dynamical behavior of the Heisenberg ferromagnet-type integrable Akbota equation (AE).
  • To derive accurate closed-form traveling wave solutions for the AE.
  • To analyze and visualize the physical characteristics of the obtained soliton solutions.

Main Methods:

  • Utilized the Kumar-Malik method for deriving solutions.
  • Employed the new Kudryashov method.
  • Applied the Riccati equation method to find analytical solutions.

Main Results:

  • Derived closed-form traveling wave solutions for the Akbota equation.
  • Obtained solutions include trigonometric, hyperbolic, and rational functions.
  • Identified precise analytical remedies for soliton waves, specifically kink, bright, and dark solitons.

Conclusions:

  • The study successfully derived various analytical solutions for the Akbota equation using multiple methods.
  • The obtained solutions represent important soliton wave phenomena like kink, bright, and dark solitons.
  • Visual representations enhance the understanding of the physical implications of these soliton solutions in nonlinear systems.