arXiv subjects

Yuhei Kogo

Publications and source records attributed to Yuhei Kogo.

2 recordsLinked to original sources

arXiv2026

Finite-Gap Solutions of the Pohlmeyer--Lund--Regge Equation and the Associated Curve Evolution

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.

math.DG↗

arXiv2025

The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation

This paper investigates the evolution of space curves governed by the Pohlmeyer-Lund-Regge (PLR) equation, an integrable extension of the sine-Gordon equation. We examine a specific type of curve evolution, known as the Lund-Regge evolution, and derive its representation in the Frenet frame. We show the Frenet frame evolution aligns with the Lax system of the PLR equation and develop a construction method for curve families via the Sym formula. In conclusion, we describe the Lund-Regge evolution corresponding the Date multi-soliton solutions to the PLR equation, with illustrations of curves and surfaces.

math.DG↗