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Nonlinear optical dynamics and complex wave structures in nonlinear dispersive media.

Samina Samina1, Maham Munawar2, Ali R Ansari3

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Summary
This summary is machine-generated.

Researchers found new optical soliton solutions for the Kairat-X equation using the generalized auxiliary equation technique. This study enhances understanding of nonlinear wave dynamics and their applications.

Keywords:
ChaosLyapunov exponentMultistabilitySensitivity analysis

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Area of Science:

  • Nonlinear optics
  • Mathematical physics

Background:

  • Optical solitons are crucial for stable signal transmission in nonlinear media.
  • Understanding their behavior is vital for advancements in telecommunications and quantum physics.
  • The Kairat-X equation models complex wave phenomena influenced by dispersion.

Purpose of the Study:

  • To derive novel soliton solutions for the nonlinear Kairat-X equation.
  • To analyze the complex dynamics of the model using advanced mathematical and computational techniques.
  • To investigate the impact of noise on system stability and sensitivity.

Main Methods:

  • Generalized auxiliary equation technique for soliton resolution.
  • Phase portraits, Lyapunov exponents, and 3D attractors for dynamic analysis.
  • Stochastic sensitivity analysis, including Poincaré and Lyapunov analysis, to assess noise effects.

Main Results:

  • Discovery of new periodic, exponential, and other soliton solutions.
  • Comprehensive examination of model dynamics revealing intricate patterns and attractors.
  • Quantification of noise intensity's influence on system sensitivity and instability.

Conclusions:

  • The generalized auxiliary equation technique effectively yields novel soliton solutions for the Kairat-X equation.
  • The detailed dynamic analysis provides deep insights into nonlinear wave behavior.
  • The findings offer significant contributions to the field of nonlinear science and optical communications.