{"product_id":"9780792363156","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003eKrasil'shchik, I.S.; Kersten, P.H.\u003c\/h2\u003e \u003cp\u003eTo 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2000-05-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792363156\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-017-3196-6\u003c\/p\u003e \u003cp\u003eDimensions: 234cm x156cm\u003c\/p\u003e \u003cp\u003ePages: 384\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46539694538892,"sku":"9780792363156","price":152.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792363156.jpg?v=1775679064","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780792363156","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}