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Advanced soliton structures and elliptic wave patterns in a sixth-order nonlinear Schrödinger equation using improved

Mina M Fahim1,2, Hamdy M Ahmed3, K A Dib4

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Area of Science:

  • Nonlinear physics
  • Optics
  • Wave propagation

Background:

  • The nonlinear Schrödinger equation (NLSE) is crucial for modeling wave phenomena.
  • Higher-order nonlinear and dispersive effects are vital in advanced optical systems.
  • Existing NLSE models may not capture complex dynamics fully.

Purpose of the Study:

  • To investigate a sixth-order integrable extension of the NLSE.
  • To model higher-order nonlinear and dispersive effects in optical systems.
  • To uncover novel analytical solutions and understand nonlinear wave behavior.

Main Methods:

  • Utilized the Improved Modified Extended Tanh Function Method.
  • Derived exact analytical solutions for the sixth-order NLSE.
  • Employed two- and three-dimensional graphical simulations for analysis.

Main Results:

  • Obtained a comprehensive family of exact analytical solutions.
  • Discovered bright solitons, dark solitons, singular solitons, and singular periodic solutions.
  • Identified new soliton and elliptic wave structures, including Jacobi and Weierstrass functions.

Conclusions:

  • The sixth-order NLSE extension reveals rich nonlinear dynamics.
  • Clarified the transition between periodic and localized wave behaviors.
  • Findings have potential implications for ultrafast optical and nonlinear waveguide technologies.