21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

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.

  1. Existence theory for solitary waves
  2. Stability and instability of solitary waves
  3. Singularity formation
  4. Initial-value and initial-boundary-value problems
  5. Incorporation of damping into nonlinear dispersive wave equations
  6. Application of the theory to problems in mechanics
21st Century COE Program : Mathematics of Nonlinear Structure via Singularity