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Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

Anjan Kundu1, Abhik Mukherjee1, Tapan Naskar1

  • 1Theory Division , Saha Institute of Nuclear Physics , Kolkata, India.

Proceedings. Mathematical, Physical, and Engineering Sciences
|April 9, 2014
PubMed
Summary

This study introduces a 2D nonlinear Schrödinger (NLS) model for rogue waves. The model accurately describes rogue wave dynamics, including adjustable height and inclination, offering a promising tool for oceanographic research.

Keywords:
exact lump solitonintegrable two-dimensional nonlinear Schrödinger equationnonlinear waverogue wave modeltopological charge

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Area of Science:

  • Fluid dynamics
  • Nonlinear physics
  • Oceanography

Background:

  • Rogue waves are extreme, unpredictable ocean surface waves.
  • Existing models are primarily 1D, limiting realistic wave representation.
  • Limited theoretical models capture rogue waves' complex 2D behavior.

Purpose of the Study:

  • To develop a 2D, exactly solvable nonlinear Schrödinger (NLS) equation for rogue wave modeling.
  • To analyze the nonlinear effects and directional preferences in rogue wave formation.
  • To provide an exact analytical model for rogue wave dynamics.

Main Methods:

  • Derivation of a 2D nonlinear Schrödinger (NLS) equation from hydrodynamic principles.
  • Utilizing integrable structures for exact solvability.
  • Analysis of modulation instability, frequency correction, and lump soliton solutions.

Main Results:

  • The 2D NLS equation accurately models rogue waves with adjustable amplitude and inclination.
  • Demonstrated modulation instability and frequency correction with directional preference.
  • Identified a lump soliton solution representing a mature rogue wave.

Conclusions:

  • The proposed 2D NLS model offers a precise analytical tool for studying ocean rogue waves.
  • The model captures key rogue wave characteristics, including dynamics influenced by ocean currents.
  • This research provides a significant advancement in theoretical rogue wave understanding.