English

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

Exactly Solvable and Integrable Systems 2025-09-23 v2

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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Cite

@article{arxiv.2503.02364,
  title  = {Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation},
  author = {Andrei Marin and Adrian Stefan Carstea},
  journal= {arXiv preprint arXiv:2503.02364},
  year   = {2025}
}

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14 pages