The principal investigator will develop and improve methods for understanding the stability of nonlinear waves as solutions of partial differential equations which arise in a number of scientific fields. In one particular case, he will use ideas he has recently developed to establish the exponential decay rate for nonlinear perturbations in solitary wave problems for KdV- type equations. The qualitative analysis of nonlinear waves for such systems is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.
