Finite-Gap Solutions of the Pohlmeyer--Lund--Regge Equation and the Associated Curve Evolution
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917439208423424 |
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| author | Kogo, Yuhei |
| author_facet | Kogo, Yuhei |
| contents | We develop a finite-gap construction for the Pohlmeyer--Lund--Regge (PLR) equation and the associated Lund--Regge curve evolution. From the hyperelliptic spectral data we build a Baker--Akhiezer function and an $\mathrm {SU}(2)$-frame, yielding an explicit theta-quotient formula for the PLR solution. We then derive criteria of the Lund-Regge curve: under natural quasi-periodicity assumptions, $s$-closure and $t$-periodicity are each equivalent to a critical-point condition for the corresponding quasimomentum differential together with a phase quantization at the reconstruction point. This provides a PLR analogue of the closure mechanism of Calini--Ivey. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-Gap Solutions of the Pohlmeyer--Lund--Regge Equation and the Associated Curve Evolution Kogo, Yuhei Differential Geometry 53A04(Primary), 37K10(Secondary) We develop a finite-gap construction for the Pohlmeyer--Lund--Regge (PLR) equation and the associated Lund--Regge curve evolution. From the hyperelliptic spectral data we build a Baker--Akhiezer function and an $\mathrm {SU}(2)$-frame, yielding an explicit theta-quotient formula for the PLR solution. We then derive criteria of the Lund-Regge curve: under natural quasi-periodicity assumptions, $s$-closure and $t$-periodicity are each equivalent to a critical-point condition for the corresponding quasimomentum differential together with a phase quantization at the reconstruction point. This provides a PLR analogue of the closure mechanism of Calini--Ivey. |
| title | Finite-Gap Solutions of the Pohlmeyer--Lund--Regge Equation and the Associated Curve Evolution |
| topic | Differential Geometry 53A04(Primary), 37K10(Secondary) |
| url | https://arxiv.org/abs/2604.24129 |