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<p>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 to the Date multi-soliton solutions to the PLR equation, with illustrations of curves and surfaces.</p>

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The Evolution of a Curve Induced by the Pohlmeyer–Lund–Regge Equation

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Shimpei Kobayashi,
  • Yuhei Kogo,
  • Nozomu Matsuura

摘要

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 to the Date multi-soliton solutions to the PLR equation, with illustrations of curves and surfaces.