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Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations - Mathematics and Its Applications 507 (Hardback)
  • Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations - Mathematics and Its Applications 507 (Hardback)
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Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations - Mathematics and Its Applications 507 (Hardback)

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Hardback 384 Pages / Published: 31/05/2000
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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.

Publisher: Springer
ISBN: 9780792363156
Number of pages: 384
Weight: 1640 g
Dimensions: 234 x 156 x 23 mm
Edition: 2000 ed.

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