A new conservation theorem
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Nail H. Ibragimov |
| Title: | A new conservation theorem |
| Journal: | Journal of Mathematical Analysis and Applications |
| Year: | 2007 |
| Volume: | 333 |
| Issue: | 1 |
| Pagination: | 311-328 |
| ISSN: | 0022-247X |
| Publisher: | Academic Press |
| ISI number: | 000247325900022 |
| 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 http://www.tek.bth.se/ |
| Authors e-mail: | nib@bth.se |
| Language: | English |
| Abstract: | A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Backlund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians. |
| Subject: | Mathematics\General Mathematics\Analysis |
| Keywords: | conservation laws |
