CONSTRUCTING INTEGRABLE 3RD-ORDER SYSTEMS - THE GAMBIER APPROACH

Authors
LAFORTUNE S GRAMMATICOS B RAMANI A
Citation
S. Lafortune et al., CONSTRUCTING INTEGRABLE 3RD-ORDER SYSTEMS - THE GAMBIER APPROACH, Inverse problems, 14(2), 1998, pp. 287-298
Citations number
11
Categorie Soggetti
Mathematics,"Physycs, Mathematical","Physycs, Mathematical",Mathematics
Journal title
Inverse problems → ACNP
ISSN journal
02665611
Volume
14
Issue
2
Year of publication
1998
Pages
287 - 298
Database
ISI
SICI code
0266-5611(1998)14:2<287:CI3S-T>2.0.ZU;2-1
Abstract
We present a systematic construction of integrable third-order systems based on the coupling of an integrable second-order equation and a Ri ccati equation. This approach is an extension of the Gambler method th at led to the equation that bears his name. Our study is carried throu gh for both continuous and discrete systems. In both cases the investi gation is based on the study of the singularities of the system (the P ainleve method for ordinary differential equations and the singularity confinement method for mappings).