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<p>By blending Painlevé property with singularity confinement for a general arbitrary order Sawada-Kotera differential-difference equation, we find a proliferation of “tau-functions” (coming from confined patterns). However, only one of these function enters into the Hirota bilinear form (the others give multi-linear expressions) but it has specific relations with all others. We also discuss two modifications of the Sawada-Kotera equation. Fully discretizations and the express method for computing algebraic entropy are discussed.</p>

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Singularity Confinement and Proliferation of Tau Functions for a General Differential-Difference Sawada-Kotera Equation

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  • 出版模式：

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  • 发表日期：

    2025年9月21日

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  • A. Marin,
  • A. S. Carstea

摘要

By blending Painlevé property with singularity confinement for a general arbitrary order Sawada-Kotera differential-difference equation, we find a proliferation of “tau-functions” (coming from confined patterns). However, only one of these function enters into the Hirota bilinear form (the others give multi-linear expressions) but it has specific relations with all others. We also discuss two modifications of the Sawada-Kotera equation. Fully discretizations and the express method for computing algebraic entropy are discussed.