Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
arXiv:solv-int/9904023 · doi:10.1088/0951-7715/12/4/313
Abstract
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 Backlund 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 Painleve 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 Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.
To appear in Nonlinearity (22 pages)
References in corpus (3)
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- The Radius of Convergence and the Well-Posedness of the Painlevé Expansions of the Korteweg-deVries equation
Cited by in corpus (7)
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- First degree birational transformations of the Painlevé equations and their contiguity relations
- New contiguity relation of the sixth Painlevé equation from a truncation
- Bäcklund Transformations for First and Second Painlevé Hierarchies
- Transformations of ordinary differential equations via Darboux transformation technique
- A truncation for obtaining all the first degree birational transformations of the Painlevé transcendents