Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations: 507 (Mathematics and Its Applications, 507) - Softcover

Krasil'shchik, I.S.; Kersten, P.H.

Softcover

ISBN 10: 904815460X ISBN 13: 9789048154609

Publisher: Springer, 2010

Synopsis

To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num­ ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation. It soon became clear that systems of such a kind possess a number of characteristic properties, such as infinite series of symmetries and/or conservation laws, inverse scattering problem formulation, L - A pair representation, existence of prolongation structures, etc. And though no satisfactory definition of complete integrability was yet invented, a need of testing a particular system for these properties appeared. Probably one of the most efficient tests of this kind was first proposed by Lenard [19]' who constructed a recursion operator for symmetries of the KdV equation. It was a strange operator, in a sense: being formally integro-differential, its action on the first classical symmetry (x-translation) was well-defined and produced the entire series of higher KdV equations; but applied to the scaling symmetry, it gave expressions containing terms of the type J u dx which had no adequate interpretation in the framework of the existing theories. It is not surprising that P. Olver wrote "The de­ duction of the form of the recursion operator (if it exists) requires a certain amount of inspired guesswork. . . " [80, p.

About this title

Review

This book is probably the most informative and highly helpful work on the subject of structural aspects of composites, and merits an honored place in the study of every student and researcher associated with composites. Practicing composite structures engineers dealing with composites cannot fail to find much of interest and motivate them in this volume. It demands a place in their libraries. Indeed a worthwhile investment that continues the level of excellence associated with the earlier edition. – Current Engineering Practice, vol. 47, 2004.

About the Author

Dr. Vinson is the H. Fletcher Brown Professor of Mechanical and Aerospace Engineering at the University of Delaware. In 1977 he received the ONR-AIAA Structural Mechanics Award for his research in composite materials, and in 1981 he was awarded an ASME Centennial Award. He is active as a consultant to government and industry. He recently received a Fellowship from the Japan Society for the Promotion of Science for 1985. He has been Chairman of the American Organizing Committee for the Japan-United States Conferences on Composite Materials three times (1981, 1983 and 1986). Dr. Sierakowski is Professor and Chairman of the Civil Engineering Department at the Ohio State University. He has held many academic and industrial posts in the United States and has been a National Research Council Senior Research Fellow, a consultant to Air Force Laboratories, and a Visiting Professor at the Air Force Office of Scientific Research.

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 904815460X
• ISBN 13: 9789048154609
• Binding: Paperback
• Number of pages: 400