Preface This book originated from lectures given by the author in January and February 2000 at IMPA’s summer program, in the months of August to December 2002 at the State University of Campinas, and in the 24o Col´ oquio Brasileiro de Matem´atica, 2003, Brazil. The intention of this book is to provide a self-contained presentation of clas- sical and new methods in the mathematical studies of wave phenomena that are related to the existence and stability of travelling wave solutions (solitary and pe- riodic waves) for nonlinear dispersive evolution equations. Although many results may be found in the existing literature, in this book we offer new results. This book has also been designed to be instructive as well as to be a new source of reference for students and for mature scientists interested in nonlinear wave phe- nomena. Simplicity and concrete applications are emphasized in order to make the material easily assimilated. Also, I hope that it inspires future developments in this important and useful subject. The preparation of this book had partial support from O Conselho Nacional de Desenvolvimento Cient´ ıfico e Tecnol´ ogico (CNPq) and from Coordena¸ de Aperfei¸ coamento de Pessoal de ıvel Superior (CAPES), which support Brazilian research. Also, my appreciation goes to the Department of Mathematics of the State University of ao Paulo, ao Paulo, Brazil (where I am a professor) and to the Department of Mathematics of the University of California, Santa Barbara, where part of this book was finished. I am indebted to many friends who gave me the initial inspiration for the treat- ment of this subject, the support, the encouragement, and suggestions to complete this book. I express my hearty thanks to Professors J. Albert, H. Biagioni, J. Bona, R. Iorio, F. Linares, and M. Scialom. Last but not least gratitude goes to my wife, Martha, who was incredibly tolerant and cooperative during the evolution of this book, and also to my daughter, Victoria Mel, who gave me part of her valuable time to finish this manuscript. Jaime Angulo Pava State University of ao Paulo May 2009 xi
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