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The answer to the question put to me by L.V. Ovsyannikov 33 years ago
Ansvarig organisation
2007 (Engelska)Konferensbidrag, Enbart muntlig presentation (Refereegranskat)
Abstract [en]

In 1973, during a discussion of the pioneering works on soliton theory at ``Theoretical seminar of the Institute of Hydrodynamics" in Novosibirsk, Professor Ovsyannikov asked me if the infinite number of conservation laws for the Korteweg-de Vries equation can be obtained from its symmetries. The answer was by no means evident because the KdV equation did not have the usual Lagrangian, and hence the Noether theorem was not applicable. In my talk I give the affirmative answer to Ovsyannikov's question by proving a general theorem on conservation laws for arbitrary differential equations. The new conservation theorem does not require existence of a Lagrangian and is based on a concept of adjoint equations for non-linear equations. For derivation of the infinites series of conservation laws for the KdV equation, I modify the notion of self-adjoint equations and extend it to non-linear equations.

Ort, förlag, år, upplaga, sidor
Karlskrona, Sweden, 2007.
Nyckelord [en]
Conservation laws, the KdV equation, self-adjoint equations
Nationell ämneskategori
Matematik Matematisk analys
Identifikatorer
URN: urn:nbn:se:bth-8709Lokalt ID: oai:bth.se:forskinfoD5406D4ABC77052FC12573C9003CA49EOAI: oai:DiVA.org:bth-8709DiVA, id: diva2:836460
Konferens
International conference MOGRAN 11
Tillgänglig från: 2012-09-18 Skapad: 2008-01-07 Senast uppdaterad: 2018-11-15Bibliografiskt granskad

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