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From rogue wave solution to solitons.

Amdad Chowdury1, Wonkeun Chang2, Marco Battiato1

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Summary
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Rogue waves transform into solitons due to third-order dispersion, self-steepening, and Raman effects. These nonlinear phenomena collectively generate multiple solitons from a single rogue wave event.

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Area of Science:

  • Nonlinear optics
  • Mathematical physics

Background:

  • Rogue waves are extreme amplitude events in nonlinear systems.
  • Understanding rogue wave transformation is crucial for nonlinear wave dynamics.

Purpose of the Study:

  • Investigate rogue wave transformation into solitons.
  • Analyze the impact of specific nonlinear effects on rogue wave dynamics.

Main Methods:

  • Generalized nonlinear Schrödinger equation.
  • Local inverse scattering technique.
  • Volume interpretation of wave solutions.

Main Results:

  • Third-order dispersion and Raman shift generate solitons.
  • Self-steepening stretches rogue waves, reducing their volume.
  • Combined effects create multiple solitons from a single rogue wave.

Conclusions:

  • Nonlinear effects like dispersion, self-steepening, and Raman shift drive rogue wave-to-soliton transformation.
  • Rogue waves can evolve into a collection of solitons.
  • The rogue wave itself can become a soliton under these conditions.