Overview
- Authors:
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I. S. Krasil’ shchik
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Independent University of Moscow and Moscow Institute for Municipal Economy, Moscow, Russia
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P. H. M. Kersten
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Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands
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Table of contents (8 chapters)
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 1-55
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 99-153
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 155-185
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 187-242
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 243-308
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 309-348
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- I. S. Krasil’ shchik, P. H. M. Kersten
Pages 349-372
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Back Matter
Pages 373-384
About this book
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.
Authors and Affiliations
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Independent University of Moscow and Moscow Institute for Municipal Economy, Moscow, Russia
I. S. Krasil’ shchik
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Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands
P. H. M. Kersten
