Solitons in Field Theory and Nonlinear Analysis
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Springer Science+Business Media, LLC
Yisong Yang
Solitons in Field Theory and Nonlinear Analysis
,
Springer
Yisong Yang Department of Applied Mathematics and Physics Polytechnie University Brooklyn, NY 11201 USA [email protected]
Mathematics Subject Classification (2000): 35JXX, 58GXX, 81EI0, 53C80 Library of Congress Cataloging-in-Publication Data Yang, Yisong. Solitons in field theory and nonlinear analysis / Yisong Yang. p. cm. - (Springer monographs in mathematics) Includes bibliographical references and index. ISBN 978-1-4419-2919-8 ISBN 978-1-4757-6548-9 (eBook) DOI 10.1007/978-1-4757-6548-9 1. Solitons. 2. Field theory (Physics) I. Title.
(Springer-Verlag New York, Inc.) QA1.A647 [QCI74.26.W28] 51O~c21
[531'.1133]
00-067919
Printed on acid-free paper. © 2001 Springer Science+Business MediaNew York
Originally published by Springer-Verlag New York, Ine. in 2001 Softcover reprint ofthe hardcover 1st edition 2001
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Science+Business Media, LLC , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Allan Abrarns; manufacturing supervised by Erica Bresler. Photocomposed copy prepared from the author's D.1EX files.
9 8 7 6 5 432 1
ISBN 978-1-4419-2919-8
SPIN 10794041
For Sheng Peter, Anna, and Julia
Preface
There are many interesting and challenging problems in the area of classical field theory. This area has attracted the attention of algebraists, geometers, and topologists in the past and has begun to attract more analysts. Analytically, classical field theory offers all types of differential equation problems which come from the two basic sets of equations in physics describing fundamental interactions, namely, the Yang-Mills equations governing electromagnetic, weak, and strong forces, reflecting internal symmetry, and the Einstein equations governing gravity, reflecting external symmetry. Naturally, a combination of these two sets of equations would lead to a theory wh ich couples both symmetries and unifies all forces, at the classical level. This book is a monograph on the analysis and solution of the nonlinear static equations arising in classical field theory. It is weIl known that many important physical phenomena are the consequences of various levels of symmetry breakings, internal or external, or both. These phenomena are manifested through the presence of locally concentrated solutions of the corresponding governing e
