文档介绍：CONTINUOUS SYMMETRIES,
LIE ALGEBRAS,
DIFFERENTIAL EQUATIONS
PUTER ALGEBRA
This page intentionally left blank
CONTINUOUS SYMMETRIES,
LIE ALGEBRAS,
DIFFERENTIAL EQUATIONS
PUTER ALGEBRA
2nd Edition
Willi-Hans Steeb
University of Iohannesburg, South Africa
rpWorld Scientific
NEW JERSEY LONDON SINGAPORE - BElJlNG SHANGHAI - HONG KONG - TAIPEI - CHENNAI
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
CONTINUOUS SYMMETRIES, LIE ALGEBRAS, DIFFERENTIAL EQUATIONS
PUTER ALGEBRA
Second Edition
Copyright © 2007 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN-13 978-981-270-809-0
ISBN-10 981-270-809-X
Printed in Singapore.
LaiFun - Continuous 1 6/20/2007, 10:49 AM
Preface
The purpose of this book is to provide prehensive introduction to the
application of continuous symmetries and their Lie algebras to ordinary
and partial differential equations. The study of symmetries of differential
equations provides important information about the behaviour of differen-
tial equations. The symmetries can be used to find exact solutions. They
can be applied to verify and develop numerical schemes. One can also