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This dissertation, Numerical Simulation of Coupled Long Wave-short Wave System With a Mismatch in Group Velocities by Chun-Kin, Poon, 潘俊健, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled Numerical Simulation of a coupled long wave-short wave system with a mismatch in group velocities submitted by Chun-Kin POON for the degree of Master of Philosophy at the University of Hong Kong in August 2005 The resonance between two short wave envelopes and a common long wave component is examined for the situation when there is a mismatch in the respective group velocities. This situation can be expected to arise in the context of wave resonances in density-stratified fluids, when many wave modes may be permitted, and also in several other analogous physical contexts. The permitted mismatch in group velocities and consequent detuning can produce a rich set of dynamics. The general nonlinear evolution equations of long wave-short wave interaction, arising from arbitrary configurations of layered or stratified fluids, are generally nonintegrable. Computational studies for the nonlinear interactions between long wave and short waves are then performed for the general case. A numerical method, the Hopscotch method, is introduced to solve the coupled set of long wave-short wave interaction equations. i This study consists of two parts. In the first part, the modulational instability of the long wave-short wave interaction system is examined. Depending on the underlying physical situations and wave modes, the group velocity mismatch between perturbations may have a marked effect on the evolution pattern of periodic solution. The ratio between the amplitude A and B may also contribute to the changes in evolution behavior. The interplay between these factors and effects is investigated and the results are summarized. In the second part, the soliton propagation is investigated. The group velocity mismatch is also found to be important in the dynamics of the resonant interaction. The mismatch in group velocities may lead to splitting or separation of pulses, depending on the initial conditions. ii DOI: 10.5353/th_b3538133 Subjects: Water waves - Mathematical modelsDifferential equations, PartialWave mechanics

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