Bäcklund transformations for higher order Painlevé equations

Date

2004

Authors

Gordoa, P. R.
Muğan, U.
Pickering, A.
Sakka, A.

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Abstract

We present a new generalized algorithm which allows the construction of Bäcklund transformations (BTs) for higher order ordinary differential equations (ODEs). This algorithm is based on the idea of seeking transformations that preserve the Painlevé property, and is applied here to ODEs of various orders in order to recover, amongst others, their auto-BTs. Of the ODEs considered here, one is seen to be of particular interest because it allows us to show that auto-BTs can be obtained in various ways, i.e. not only by using the severest of the possible restrictions of our algorithm. © 2004 Elsevier Ltd. All rights reserved.

Source Title

Chaos, Solitons and Fractals

Publisher

Pergamon Press

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Published Version (Please cite this version)

Language

English