@article{Tao2008WhyAS,
title={Why are solitons stable},
author={T. Tao},
journal={Bulletin of the American Mathematical Society},
year={2008},
volume={46},
pages={1-33}
}

The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account, \emph{solitary wave} or \emph{soliton} solutions can be created, which can be stable enough to persist indefinitely. The construction of such solutions is relatively straightforward, but the fact that they are \emph{stable} requires some significant amounts of… CONTINUE READING