Laplace type invariants for parabolic equations
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Nail H. Ibragimov |
| Title: | Laplace type invariants for parabolic equations |
| Journal: | NONLINEAR DYNAMICS |
| Year: | 2002 |
| Pagination: | 125-133 |
| ISSN: | 0924-090X |
| Publisher: | KLUWER ACADEMIC PUBL |
| City: | DORDRECHT |
| ISI number: | 000174933300003 |
| 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/ |
| Language: | English |
| Abstract: | The Laplace invariants pertain to linear hyperbolic differential equations with two independent variables. They were discovered by Laplace in 1773 and used in his integration theory of hyperbolic equations. Cotton extended the Laplace invariants to elliptic equations in 1900. Cotton's invariants can be obtained from the Laplace invariants merely by the complex change of variables relating the elliptic and hyperbolic equations. To the best of my knowledge, the invariants for parabolic equations were not found thus far. The purpose of this paper is to fill this gap by considering what will be called Laplace type invariants (or seminvariants), i.e. the quantities that remain unaltered under the linear transformation of the dependent variable. Laplace type invariants are calculated here for all hyperbolic, elliptic and parabolic equations using the unified infinitesimal method. A new invariant is found for parabolic equations. |
| Subject: | Mathematics\General Mathematics\Analysis |
| Keywords: | hyperbolic, elliptic and parabolic equations, equivalence transformation, seminvariants, Laplace type invariants |
