Seminar talk, 21 October 2020: Difference between revisions
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| title = A converse to Noether's theorem | | title = A converse to Noether's theorem | ||
| abstract = The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement. | | abstract = The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement. | ||
Language: English | |||
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Revision as of 14:52, 13 October 2020
Speaker: Markus Dafinger
Title: A converse to Noether's theorem
Abstract:
The classical Noether's theorem states that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. It is a well-known statement to physicists with many applications. In the talk we investigate a reverse statement, namely that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation. The aim of the talk is to provide some background of the so-called inverse problem of the calculus of variations and then to discuss some new results, for example, how to prove the reverse statement.
Language: English