zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Lagrangian approach to evolution equations: symmetries and conservation laws. (English) Zbl 1106.70012
This paper describes a method to derive conservation laws for some evolution equations. Given an evolution equation non admitting a Lagrangian description, then, if there exists a new evolution equation in a new dependent variable or field in such a way that one can find a Lagrangian formulation for the coupled system of evolution equations, the study of Lagrangian symmetries for the new system can be used in order to obtain conservation laws, via Noether’s theorem, for the original problem. By using this method, the authors give Lagrangian descriptions of heat equation, Burgers equation, nonlinear heat equation, and nonlinear Schrödinger and Korteweg-de Vrieg type systems. As a first example, the infinite set of known conservation laws of heat equation is described by applying Noether’s theorem. Next, the method is applied to the nonlinear heat equation, as well as to Burgers equation, and new non-local conservation laws are obtained.

70H33Symmetries and conservation laws, reverse symmetries, invariant manifolds, etc.
70G65Symmetries, Lie-group and Lie-algebra methods for dynamical systems
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
Full Text: DOI