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Rogue wave modes for a derivative nonlinear Schrödinger model.
Hiu Ning Chan1, Kwok Wing Chow1, David Jacob Kedziora2
1Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong.
Summary
Rogue waves in derivative nonlinear Schrödinger equations can occur with negative cubic nonlinearity, linked to modulation instability. Their maximum amplitude is three times the background, matching Peregrine breather results.
Area of Science:
- Fluid dynamics
- Nonlinear optics
- Wave phenomena
Background:
- Rogue waves are large, unexpected wave displacements.
- They appear in nonlinear Schrödinger equations with specific nonlinearity and dispersion regimes.
Purpose of the Study:
- To investigate rogue waves in a derivative nonlinear Schrödinger equation.
- To explore their occurrence in negative cubic nonlinearity regimes.
- To connect rogue wave formation with modulation instability.
Main Methods:
- Calculated rogue waves as a long-wave limit of a breather.
- Analyzed the role of self-steepening nonlinearity.
- Investigated the threshold for modulation instability.
- Performed numerical simulations.
Main Results:
- Rogue waves can occur in negative cubic nonlinearity with sufficient self-steepening.
- The critical self-steepening magnitude matches the modulation instability threshold.
- Maximum rogue wave amplitude is three times the background amplitude.
- Results correlate with experimental water wave data.
Conclusions:
- Rogue waves in this model are strongly linked to modulation instability.
- The findings provide a theoretical basis for rogue wave occurrence in diverse nonlinear systems.
- The study bridges theoretical calculations with experimental observations.
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