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arXiv · 2504.05733

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

Shimpei Kobayashi·Yuhei Kogo·Nozomu Matsuura
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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.

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Shimpei Kobayashi, Yuhei Kogo, Nozomu Matsuura. 2025-06-28. The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation. https://arxiv.org/abs/2504.05733

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