Discrete equations and the singular manifold method

Details Discrete equations and the singular manifold method Discrete equations and the singular manifold method

1999-03-29

arxiv.org/abs/solv-int/9904002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

to appear in SIDE III proceedings

Scientific paper

The Painleve expansion for the second Painleve equation (PII) and fourth Painleve 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 Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.

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