Finite Dimensional Integrable Nonlinear Dynamical Systems
We have seen in the earlier chapters that dynamical equations of typical nonlinear systems are not amenable to exact solutions in terms of known functions, except for isolated cases like the equations of motion of the undamped and unforced Duffing oscilla
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Advanced Texts in Physics This program of advanced texts covers a broad spectrum of topics which are of current and emerging interest in physics. Each book provides a comprehensive and yet current and emerging interest in physics. Each book provides a comprehensive and yet accessible introduction to a field at the forefront of modern research. As such, these texts are intended for senior undergraduate and graduate students at the MS and PhD level; however, research scientists seeking an introduction to particular areas of physics will also benefit from the titles in this collection.
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M. Lakshmanan
S. Rajasekar
Nonlinear Dynamics Integrability, Chaos, and Patterns
With 193 Figures, 17 Tables, Numerous Examples and Problems
"
Springer
Professor M. Lakshmanan
Dr. S. Rajasekar
Department of Physics and Center for Nonlinear Dynamics Bharathidasan University Tiruchirapalli - 620 024 India
Department of Physics Manonmaniam Sundaranar University Tirunelveli - 627 012 India
Library of Congress Cataloging-in-Publication Data. Lakshmanan, M. (Muthuswamy) Nonlinear dynamics : integrability, chaos, and patterns / M. Lakshmanan; S. Rajasekar. p. cm - (Advanced texts in physics, ISSN 1439-2674) Includes bibliographical references and index. ISBN 978-3-642-62872-6 ISBN 978-3-642-55688-3 (eBook) DOI 10.1007/978-3-642-55688-3
1. Dynamics. 2. Nonlinear theories. 1. Rajasekar, S. (Shanmuganathan), 1963- II. Title. III Series. QA845.L252002 531'.11-dc21 2002030441
ISSN 1439-2674
ISBN 978-3-642-62872-6 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-Verlag. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003
Originally published by Springer-Verlag Berlin Heidelberg in 2003 Softcovcr reprint of the hanlcover lst edition 2003
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. Typesetting: Data prepared by the authors using a Springer TiC macro package Final page layout: EDV-Beratung Frank Herweg, Leutershausen Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN 10884430
57/3141/tr
54 321o
To our parents
Preface
Nonlinearity is ubiquitous and all pervading in the physical world. For a long time nonlinear systems were essentially studied under linear
