Loading...
Please wait, while we are loading the content...
Similar Documents
Existence and Uniqueness Theorems for Formal Power Series Solutions of Analytic Diierential Systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Rust, C. J. Reid, Gregory J. Wittkopf, Allan D. |
| Copyright Year | 1999 |
| Abstract | We present Existence and Uniqueness Theorems for formal power series solutions of analytic systems of pde in a certain form. This form can be obtained by a nite number of diierentiations and eliminations of the original system, and allows its formal power series solutions to be computed in an algorithmic fashion. The resulting reduced involutive form (rif 0 form) produced by our rif 0 algorithm is a generalization of the classical form of Riquier and Janet, and that of Cauchy{ Kovalevskaya. We weaken the assumption of linearity in the highest derivatives in those approaches to allow for systems which are nonlinear in their highest derivatives. A new formal development of Riquier's theory is given, with proofs, modeled after those in Grr obner Basis Theory. For the nonlinear theory, the concept of relative Riquier Bases is introduced. This allows for the easy extension of ideas from the linear to the nonlinear theory. The essential idea is that an arbitrary nonlinear system can be written (after diierentiation if necessary), as a system which is linear in its highest derivatives, and a constraint system, which is nonlinear in its highest derivatives. Our theorems are applied to several examples. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.cecm.sfu.ca/~reid/ReidPapers/RustReidWittkopf99.ps.gz |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
