Introduction to nonlinear science

the long version

The aim of this book is to develop a unified approach to nonlinear science which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate the development of the subject by physical examples and prototypical experiments, and the mathematical techniques by reference to simple models. Each chapter concludes with a set of problems. . This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications, as well as to researchers and teachers involved in one way or another in this field.