Applications of Symmetry Methods to Partial Differential Equations
This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mapping
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168
Applications of Symmetry Methods to Partial Differential Equations
Applied Mathematical Sciences Volume 168 Editors S.S. Antman J.E. Marsden L. Sirovich
Advisors J.K. Hale P. Holmes J. Keener J. Keller B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan
For further volumes: http://www.springer.com/series/34
George W. Bluman Alexei F. Cheviakov Stephen C. Anco
Applications of Symmetry Methods to Partial Differential Equations
George W. Bluman Department of Mathematics The University of British Columbia Vancouver, British Columbia V6T 1Z2 Canada [email protected]
Alexei F. Cheviakov Department of Mathematics and Statistics University of Saskatchewan Saskatoon SK S7N 5E6 Canada [email protected]
Stephen C. Anco Department of Mathematics Brock University St. Catharines, Ontario L2S 3A1 Canada [email protected]
Editors: S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park MD 20742-4015 USA [email protected]
J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA [email protected]
L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574 USA [email protected]
ISSN 0066-5452 ISBN 978-0-387-98612-8 e-ISBN 978-0-387-68028-6 DOI 10.1007/978-0-387-68028-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009937642 Mathematics Subject Classification (2000): 58J70, 70H33, 35A30, 58J72, 35A20, 35A10, 35A15, 35A25, 70H06 © Springer Science+Business Media, LLC 2010 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, 233 Spring Street, New York, NY 10013, USA), 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1
Local Transformations and Conservation Laws . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Local Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Point transformations . . . . . . . . . . . . . . . . . . . . .
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