The answer to the question put to me by L.V. Ovsyannikov 33 years ago

Document type: Conference Presentations
Peer reviewed: Yes
Author(s): Nail H. Ibragimov
Title: The answer to the question put to me by L.V. Ovsyannikov 33 years ago
Conference name: International conference MOGRAN 11
Year: May 27-June 2, 2007
City: Karlskrona, Sweden
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: 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.
Subject: Mathematics\Analysis
Keywords: Conservation laws, the KdV equation, self-adjoint equations