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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
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Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations

Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations

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

Hardcover

Series: Mathematics and Its Applications, Book 507

Medical ReferenceAlgebraGeneral Mathematics

ISBN10: 0792363159
ISBN13: 9780792363156
Publisher: Springer Nature
Published: May 31 2000
Pages: 384
Weight: 1.56
Height: 1.17 Width: 6.56 Depth: 9.42
Language: English
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.

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