Discrete equations and the singular manifold method
P. G. Estevez (Universidad de Salamanca, Spain), P.A. Clarkson, (University of Kent at Canterbury, UK)
TL;DR
This paper develops a double singular manifold method to derive Miura and auto-Backlund transformations for Painleve equations, enabling the construction of related discrete equations.
Contribution
It introduces a novel double singular manifold approach to connect Painleve equations with discrete systems through transformations.
Findings
Derived Miura transformations for PII and PIV
Obtained auto-Backlund transformations for these equations
Constructed discrete equations from transformations
Abstract
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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Taxonomy
TopicsNonlinear Waves and Solitons · Geometric Analysis and Curvature Flows · Advanced Numerical Analysis Techniques