| Abstract: |
| Lax and Levermore showed that solutions of the Korteweg-de Vries equation in the small-dispersion limit exhibit rapid oscillations within slowly modulated envelopes. Similar behavior has been shown for other integrable soliton equations, such as focusing NLS and sine-Gordon, using so-called semiclassical soliton ensembles, which are pure soliton intial data intended to approximate more general initial data in the zero-dispersion limit. We will present recent analytical and numerical results on semiclassical solitons ensembles for the three-wave resonant interaction equations. Despite the fact that these equations are non-dispersive, many of the qualitative behaviors are the same as for dispersive equations. We will also show how our results for the three-wave resonant interaction equations can be used to better understand solutions of the focusing NLS equation with compactly supported initial data. |
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