Nonlinear self-adjointness and conservation laws
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Nail H. Ibragimov |
| Title: | Nonlinear self-adjointness and conservation laws |
| Journal: | Journal of Physics A: Mathematical and Theoretical |
| Year: | 2011 |
| Volume: | 44 |
| Issue: | 43 |
| Pagination: | Article number 432002 |
| ISSN: | 1751-8113 |
| Publisher: | IOP Science |
| URI/DOI: | 10.1088/1751-8113/44/43/432002 |
| ISI number: | 000296147000002 |
| Organization: | Blekinge Institute of Technology |
| Department: | School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap) School of Engineering S-371 79 Karlskrona +46 455 38 50 00 http://www.bth.se/ing/ |
| Language: | English |
| Abstract: | The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut u = 0 becomes strictly self-adjoint after multiplying by u1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems. |
| Subject: | Mathematics\General |
