Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909799048806400 |
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| author | Marin, Andrei Carstea, Adrian Stefan |
| author_facet | Marin, Andrei Carstea, Adrian Stefan |
| contents | 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation Marin, Andrei Carstea, Adrian Stefan Exactly Solvable and Integrable Systems 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 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. |
| title | Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.02364 |