## Jerry Bona : Nonlinear Dispersive Equations, Expository Lectures

### Derivation and some fundamental properties of nonlinear dispersive waves equations

### Abstract

This series of lectures aims to introduce some of the
principal aspects of nonlinear dispersive wave theory.
We start with an appreciation of the early history, and
then introduce, within the original fluid mechanics
context, the paradigm Korteweg-de Vries equation. Some
of the more important properties of this equation are
then outlined. These properties motivate and give direction
to the further study of this and other nonlinear dispersive
wave equations.

Further issues to be addressed will be chosen from among
the following topics.

- Existence theory for solitary waves
- Stability and instability of solitary waves
- Singularity formation
- Initial-value and initial-boundary-value problems
- Incorporation of damping into nonlinear dispersive wave equations
- Application of the theory to problems in mechanics