A solitary wave is a localized coherent structure that maintains its shape while it travels at constant speed. They are caused by a cancellation of nonlinear and dispersive effects in the medium. In this talk, we discuss a special type of solitary waves: wavepacket solitary waves. In contrast to the celebrated KdV soliton, wavepacket solitary waves have intrinsic length scale and feature oscillatory decaying tails. Two examples, capillary-gravity waves and flexural-gravity waves, will be presented to illustrate the importance of these coherent structures. 
For the capillary-gravity wave problem, the combination of geometric and nonlinear self-interaction focussing phenomenon will be discussed. In the small amplitude limit, this is well described by the 2+1 focussing nonlinear Schrodinger equation, which predicts an instability with finite-time blowup. However, we show that in the full fluid equations, the focussing is arrested, and instead, wavepacket solitary waves are generated.
The second problem that we will focus on is the flexural-gravity problem, a model for the dynamics of waves under large floating structures. Even though small amplitude solitary waves are not predicted to exist by standard perturbation analyses, we find large amplitude wavepacket solitary waves, and explore their crucial role in the forced problem of a moving load on the surface. This is meant to represent a model of the use of extended ice sheets as roads and aircraft runways.

This talk is supported by the Tsinghua Global Scholars Fellowship Program.