The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation
Differential Geometry
2025-07-01 v2 Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2504.05733,
title = {The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation},
author = {Shimpei Kobayashi and Yuhei Kogo and Nozomu Matsuura},
journal= {arXiv preprint arXiv:2504.05733},
year = {2025}
}