zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new conservation theorem. (English) Zbl 1160.35008
A classical result in the calculus of variations is the Noether theorem that every variational symmetry has an associated conservation law. The author proposes an extension of this result to arbitrary differential equations not necessarily of a variational nature. It is based on a novel concept of adjoint for nonlinear equations. The author shows first that the system consisting of the original equation plus its adjoint is variational and then that every symmetry of the original equation can be extended to one of the combined system. Now a straightforward application of the classical Noether theorem yields a conservation law. As the definition of a nonlinear adjoint requires the introduction of additional unknown functions, one obtains in general even an infinite familiy of conservation laws parametrised by solutions of the adjoint equation. As concrete examples the heat and the Korteweg-de Vries equations are studied.

MSC:
35A30Geometric theory for PDE, characteristics, transformations
58J70Invariance and symmetry properties