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arXiv · 2503.02364

Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation

Andrei Marin·Adrian Stefan Carstea
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Abstract

Blending Painlev\'e property with singularity confinement for a general arbitrary order Sawada-Kotera differential-difference equation, we find a proliferation of ``tau-functions'' (coming from strictly confined patterns). However only one of these function enters into the Hirota bilinear form (the others give multi-linear expressions) but has specific relations with all others. We also discuss the case of two modifications of Sawada-Kotera showing that periodic patterns appear in addition to strictly confined ones. Fully discretisations and express method for computing algebraic entropy are discussed.

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Andrei Marin, Adrian Stefan Carstea. 2025-03-04. Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation. https://doi.org/10.1007/s11040-025-09524-0

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