Rogue Waves in Systems with Multiple Waveguides
Professor Chow, Kwok Wing (Principal investigator)
Professor Grimshaw Roger H. J. (Co-Investigator)
Nonlinear, Rogue, Waves, Multiple, Waveguides
RGC General Research Fund (GRF)
HKU Project Code
General Research Fund (GRF)
1) To study rogue waves using a combination of theoretical and computational approaches - Rogue waves of one component NLSE have been observed experimentally in hydrodynamic wave tanks and optical fibers. Analytical information for coupled waveguides can potentially be tested in a laboratory. Discovering conditions to 'tame' rogue waves will be a great intellectual challenge; 2) To investigate the rich dynamics in systems with coupled waveguides - The properties of localized modes in any waveguide may be dramatically affected by the presence of modes in the other waveguide. Illustrative examples: (a) Coupled nonlinear Schrodinger equations - applicable to surface waves in fluid mechanics and optical fibers with carrier waves of distinct frequencies; (b) Coupled long wave-short wave resonance model - applicable to systems where the phase velocity of the long wave matches the group velocity of two (or more) short waves; 3) To recognize a quantitative indicator for rogue waves - Modulation instability, exponential growth of small disturbances resulting from the interplay of dispersive and nonlinear effects, has been closely identified with the onset of rogue waves. This correlation will be tested quantitatively in several systems of coupled waveguides; 4) To incorporate the effects of shear currents and realistic oceanic conditions - In practice oceanic free surface waves evolve under the influence of a huge variety of environmental factors and agents. We shall concentrate on the effect of shear currents. A linear shear permits analytical advances but may suffer from discontinuity in other properties of fluid dynamics. We shall study parabolic and exponential shear profiles fitted to realistic conditions, which might produce more desirable outcomes. The additional efforts are numerical computations of the vertical structure of the eigenfunctions; 5 To conduct computational studies of stability - Although there have been many derivations of the fundamental and higher order rogue wave modes in the past few years, their stability properties have received comparatively little attention. We shall address this issue. A computer simulation on the evolution of a perturbed wave profile will be conducted. It might be difficult to observe those modes with significantly distorted growth phase, as they are masked by the background modulation instability; 6) To extend the considerations to other models of dynamics - (a) 'Nonlocal' evolution equations, where the nonlinearity depends on properties of a medium not confined to the immediate spatial neighborhood of the observer: A nonlocal nonlinear Schrodinger equation solvable by the inverse scattering transform will be investigated by the present formulation. (b) Evolution systems consisting of a slowly varying complex envelope coupled to a scalar potential: We shall choose examples with bilinear forms and elucidate the dynamics of the rogue waves.