The answer to the question put to me by L.V. Ovsyannikov 33 years ago
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural SciencesMay 27 (English)Conference paper, Presentation (Refereed) Published
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.
Place, publisher, year, edition, pages
Karlskrona, Sweden, May 27.
Conservation laws, the KdV equation, self-adjoint equations
Mathematics Mathematical Analysis
IdentifiersURN: urn:nbn:se:bth-8709Local ID: oai:bth.se:forskinfoD5406D4ABC77052FC12573C9003CA49EOAI: oai:DiVA.org:bth-8709DiVA: diva2:836460
International conference MOGRAN 11