Integrability of Nonlinear Systems

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Editors Yvette Kosmann-Schwarzbach Centre de Mathématiques École Polytechnique Palaiseau 91128 Palaiseau, France Basil Grammaticos GMPIB, Université Paris VII Tour 24-14, 5 e étage, case 7021 2 place Jussieu 75251 Paris, France K. M. Tamizhmani Department of Mathematics Pondicherry University Kalapet Pondicherry 605 014, India Y. Kosmann-Schwarzbach, B. Grammaticos, K. M. Tamizhmani (eds.), Integrability of Nonlinear Systems, Lect. Notes Phys. 638 (Springer-Verlag Berlin Heidelberg 2004), DOI 10.1007/b94605 Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de ISSN 0075-8450 ISBN 3-540-20630-2 Springer-Verlag Berlin Heidelberg New York 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. Springer-Verlag is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Printed in Germany 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: Camera-ready by the authors/editor Data conversion: PTP-Berlin Protago-TeX-Production GmbH Cover design: design & production,Heidelberg Printed on acid-free paper 54/3141/du-543210
Lecture Notes in Physics Editorial Board R. Beig, Wien, Austria B.-G. Englert, Singapore U. Frisch, Nice, France P. Hänggi, Augsburg, Germany K. Hepp, Zürich, Switzerland W. Hillebrandt, Garching, Germany D. Imboden, Zürich, Switzerland R. L. Jaffe, Cambridge, MA, USA R. Lipowsky, Golm, Germany H. v. Löhneysen, Karlsruhe, Germany I. Ojima, Kyoto, Japan D. Sornette, Nice, France, and Los Angeles, CA, USA S. Theisen, Golm, Germany W. Weise, Trento, Italy, and Garching, Germany J. Wess, München, Germany J. Zittartz, Köln, Germany 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo
Page 1: Y. Kosmann-Schwarzbach B. Grammatic
Page 5: Preface This second edition of Inte
Page 8 and 9: VIII Contents 9 Applying the Confin
Page 10 and 11: X Contents Eight Lectures on Integr
Page 12 and 13: XII List of Contributors Marco Pedr
Page 14 and 15: 2 The Editors 1 Analytic Methods Th
Page 16 and 17: 4 The Editors brackets. This fundam
Page 18 and 19: 6 M.J. Ablowitz ∂φ + gη =0 on z
Page 20 and 21: 8 M.J. Ablowitz The quasilinear equ
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Page 32 and 33: 20 M.J. Ablowitz i.e., KPII, then (
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Integrability - and How to Detect I
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3.2 Partial and Constrained Integra
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8 Singularity Confinement: The Disc
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and we obtain, Integrability - and
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Introduction to the Hirota Bilinear
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3.3 Multi-soliton Solutions Introdu
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108 Y. Kosmann-Schwarzbach vector s
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110 Y. Kosmann-Schwarzbach volume,
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112 Y. Kosmann-Schwarzbach Since, w
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114 Y. Kosmann-Schwarzbach An alter
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116 Y. Kosmann-Schwarzbach define a
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118 Y. Kosmann-Schwarzbach e 1 = (
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120 Y. Kosmann-Schwarzbach r(ξ)(η
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122 Y. Kosmann-Schwarzbach The last
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124 Y. Kosmann-Schwarzbach Now 〈s
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126 Y. Kosmann-Schwarzbach 2.3 Tens
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128 Y. Kosmann-Schwarzbach or, in t
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130 Y. Kosmann-Schwarzbach Thus, by
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132 Y. Kosmann-Schwarzbach Note tha
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134 Y. Kosmann-Schwarzbach Definiti
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136 Y. Kosmann-Schwarzbach If, in p
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138 Y. Kosmann-Schwarzbach we obtai
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140 Y. Kosmann-Schwarzbach Let G be
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142 Y. Kosmann-Schwarzbach for all
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144 Y. Kosmann-Schwarzbach parallel
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146 Y. Kosmann-Schwarzbach = d ds f
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148 Y. Kosmann-Schwarzbach Taking i
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150 Y. Kosmann-Schwarzbach By the t
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152 Y. Kosmann-Schwarzbach where
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154 Y. Kosmann-Schwarzbach Example
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156 Y. Kosmann-Schwarzbach Definiti
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158 Y. Kosmann-Schwarzbach 4.8 Mome
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160 Y. Kosmann-Schwarzbach Let g be
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162 Y. Kosmann-Schwarzbach where th
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164 Y. Kosmann-Schwarzbach defining
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166 Y. Kosmann-Schwarzbach For any
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168 Y. Kosmann-Schwarzbach Proposit
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170 Y. Kosmann-Schwarzbach 3. O. Ba
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172 Y. Kosmann-Schwarzbach 39. Y. K
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Analytic and Asymptotic Methods for
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This gives Analytic and Asymptotic
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Eight Lectures on Integrable System
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• they preserve the Poisson brack
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The Poisson tensors P 0 and P 1 are
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4th Lecture: Gel’fand-Dickey Mani
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After an integration by parts, we f
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starting from h (0) = 1. A simple c
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Bilinear Formalism in Soliton Theor
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Quantum and Classical Integrable Sy
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g ++ D Quantum and Classical Integr
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Let ( V k (λ,0) Quantum and Classi
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