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The aim of this book is to give a self-contained introduction to the mathe matical analysis and physical explanations of some basic nonlinear wave phe nomena. This volume grew out of lecture notes for graduate courf; es which I gave at the University of Alberta, the University of Saskatchewan, .and Texas A&M University. As an introduction it is not intended to be exhaustive iQ its choice of material, but rather to convey to interested readers a basic; yet practical, methodology as well as some of the more important results obtained since the 1950's. Although the primary purpose of this volume...