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Orazio Descalzi • Marcel Clerc • Stefania Residori Gaetano Assanto Editors

Localized States in Physics: Solitons and Patterns

Editors Orazio Descalzi Universidad de los Andes Facultad de Ingeniería y Cs. Aplicadas Av. San Carlos de Apoquindo 2200 Las Condes Santiago Chile [email protected] Stefania Residori Institut Non-linéaire de Nice route de Lucioles 1361 06560 Valbonne France [email protected]

Marcel Clerc Universidad de Chile Fac. de Cs. Físicas y Mat. Depto. de Física Casilla 487 - 3 Santiago Chile [email protected] Gaetano Assanto University Roma Tre Nonlinear Optics and OptoElectronics Lab Via della Vasca Navale 84 00146 Roma Italy [email protected]

ISBN 978-3-642-16548-1 e-ISBN 978-3-642-16549-8 DOI 10.1007/978-3-642-16549-8 Springer Heidelberg Dordrecht London New York © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Physical systems driven far from thermodynamic equilibrium can give rise to a variety of dissipative spatial structures through spontaneous breaking of symmetries. A fascinating feature of these pattern-forming systems is their tendency to originate spatially confined states. Such localized states can exist as wave packets or propagating entities through space and/or time. Observed in many different branches of science, localized states appear to be ubiquitous in nature and characterized by common macroscopic properties, independently of the specific physical laws governing the underlying field and/or matter interactions. Even though Localized States in Physics can be found in such different domains as hydrodynamics, optics, granular matter, reaction-diffusion systems, neural networks, plasmas, Bose-Einstein condensates etc., books on the topic are still very rare and often devoted to a particular type. This Book is based on a series of lectures given at a workshop on the subject: it reflects the spirit and the breadth of the meeting, held in 2008 at the University of los Andes, Santiago, Chile. Its main motivations stem from the need to bring together - coolate and compare - various approaches