| Автор | Pilar R Gordoa |
| Автор | Nalini Joshi |
| Автор | Andrew Pickering |
| Дата выпуска | 1999-07-01 |
| dc.description | The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Bäcklund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painlevé equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Bäcklund transformations for the equations considered. We are also able to derive Bäcklund transformations onto other ODEs in the Painlevéclassification. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations |
| Тип | paper |
| DOI | 10.1088/0951-7715/12/4/313 |
| Electronic ISSN | 1361-6544 |
| Print ISSN | 0951-7715 |
| Журнал | Nonlinearity |
| Том | 12 |
| Первая страница | 955 |
| Последняя страница | 968 |
| Аффилиация | Pilar R Gordoa; Department of Pure Mathematics, University of Adelaide, Adelaide, Australia 5005 |
| Аффилиация | Nalini Joshi; Department of Pure Mathematics, University of Adelaide, Adelaide, Australia 5005 |
| Аффилиация | Andrew Pickering; Department of Pure Mathematics, University of Adelaide, Adelaide, Australia 5005 |
| Выпуск | 4 |
