M ar 1 99 9 Discrete equations and the singular manifold method
نویسندگان
چکیده
The Painlevé expansion for the second Painlevé equation (PII) and fourth Painlevé equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painlevé type equations for which auto-Bäcklund transformations are obtained. These auto-Bäcklund transformations can be used to obtain discrete equations.
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