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Painlevé Analysis for Nonlinear Partial Differential Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Musette, Micheline |
| Copyright Year | 1999 |
| Abstract | The Painleve analysis introduced by Weiss, Tabor, and, Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDEs) is an extension of the method initiated by Painleve and Gambier at the beginning of this century for the classification of algebraic nonlinear differential equations (ODEs) without movable critical points. In this chapter we explain the WTC method in its invariant version introduced by Conte in 1989 and its application to solitonic equations in order to find algorithmically their associated Backlund transformations. Many remarkable properties are shared by these so-called integrable equations, but they are generically no longer valid for equations modeling physical phenomena. Belonging to this second class, some equations called “partially integrable” sometimes keep remnants of integrability. In that case, the singularity analysis may also be useful for building closed-form analytic solutions, which necessarily agree with the singularity structure of the equations. We display the privileged role played by the Riccati equation and systems of Riccati equations that are linearizable, as well as the importance of the Weierstrass elliptic function, for building solitary waves or more elaborate solutions. |
| Starting Page | 517 |
| Ending Page | 572 |
| Page Count | 56 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/978-1-4612-1532-5_8 |
| Alternate Webpage(s) | http://arxiv.org/pdf/solv-int/9804003v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/978-1-4612-1532-5_8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
